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NDUCTIVE LOGIG

Ballantine

LIBRARY OF CONGRESS.

Cliap.Ac..'_, Copyright No.,.
Shelf_.B-2j

UNITED STATES OF AMERICA.

Inductive Logic

WM. G. BALLANTINE

President of Oberlin College

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Boston, U.S.A., and London

GINN & COMPANY, PUBLISHERS

18.96

THE LlBRAItY
OF CONGRfiftft

WA9HINGTOII

PREFACE,

^^g-^

This book originated in the class-room, where the
author was teaching Dr. Fowler's Elements of Induc-
tive Logic. Its ambition is to reproduce some of the
excellences of that bright and interesting book, while
substituting a sounder analysis of fundamental princi-
ples. The numerous extracts, introduced in the man-
ner of Dr. Fowler, are designed both to elucidate the
subject and to acquaint the student with the views and
literary styles of a large variety of philosophical and
scientific writers. Wherever anything has been found
already well expressed, quotation has been preferred to
restatement. The familiar manuals of inductive logic
have been freely drawn upon, and their rich store of
illustrations has been used without hesitation. Credit
has generally been given ; but sometimes it was impos-
sible to make specific acknowledgment.

Mr. Mill is the greatest of all modern writers upon
inductive logic, and upon his famous work all later
authors have largely built. The school manuals are,
for the most part, but outlines of his doctrine. But
Mr. Mill's mind was a very peculiar one. It was impos-
sible for one so acute not to see the truth, or for one so

iv Preface.

candid not to state it. But these statements of truth

are rather his obiter dicta, while his main contention is

often some paradox. A "higher critic" might easily

divide the Logic into two documents, by authors of

opposing tendencies. An outline of Mill's system, like

Dr. Fowler's, does him injustice ; for it is just in what

he thinks most important, that he is weakest. Freely

acknowledging that most of what is true in this book

has been learned from Mr. Mill, the author yet puts it

forth with the hope that it will be found to contain a

real, though small, contribution to the progress of

science.

Oberlin, Ohio,

December i, 1895.

CONTENTS.

-^2-^

CHAPTER I.
Introductory

Inductive Logic defined, i. The pure sciences, i. The applied
sciences, 2, Inductive and Deductive Logic not mutually exclusive, 2.
Relations of Inductive and Deductive Logic, 3. The discovery of facts
defined, 4. Quotation from Whately, 4.

CHAPTER II.

Facts 6

A fact defined, 6. Substantive facts and facts of relation, 6. Facts of
Resemblance, 7. Facts of Coexistence, 7. Facts of Causation, 7. Facts
of Succession, 8. Ultimate facts, 8.

CHAPTER III.

Observation 9

Observation defined, 9. Bagon quoted, 9. Observation the essential
characteristic of Induction, 9. Observation and Experiment contrasted,

10. Fowler quoted, 10. Difficulty of making trustworthy observations,

11. Dr. Darwin's supposed gin, 11. Confusion of perceptions and in-
ferences, 12,

CHAPTER IV.
Primary Inductions 14

An Induction defined, 14. Various kinds of inductions, 14. Uniform-
ities in the existing order, 15. How we discover a uniformity, 15. The
mill and stream, 16. Cliffs and crows of England, 17, Does induction
rest upon the veracity of God ? 17. Inductio per Enwnerationetn Sim-
plicem, 17. Correcting one generalization by another, 19. Uniformity
of Nature defined, 19. Degrees of assurance in primary inductions, 20.

vi Contents.

PAGE

Bain's definition of induction, 21. Bain's view discussed, 23. Great
inductions of modern science, 24. Empirical and ultimate laws, 25. The
maxim that " the exception proves the rule," 25.

CHAPTER V.

Secondary Inductions 28

A secondary induction defined, 28, Primary and secondary inductions
mingled in every-day thinking, 29. Whately provided only for secondary
inductions, 30. Uniformity of all nature not a necessary premise, 31.
Failure of philosophers to recognize three classes of inductions, 31.
Minto's criticism of Mill, 33. Inferring from particulars to particu-
lars, 34.

CHAPTER VI.

Mixed Inductions 36

A mixed induction defined, 36. Masts of ships seen first, 36. Newton's
discoveries, 36. The phases of Venus, 37. Mill's questions, 38, In-
duction from a single instance, 39. Correctly defining the field, 40.

CHAPTER VII.

P^ACTS OF Resemblance 41

Resemblances in objects, 41. The possibility of language, 42. Argu-
ments from facts of resemblance, 42. Anima and dme^ 43. Genesis of
the horse, 44.

CHAPTER VIII.
Facts of Coexistence 47

Illustration from gold, 47. Coexistence as important as Causation, 47.
Natural kinds and artificial kinds, 48. Infima species and stmimum
ge7ius, 49. The true nature of species discussed by Asa Gray, 49.
Agassiz's view, 50. Darwin's view, 5 1 . Linnaeus's definition, 51. Classi-
fication, 52. Nomenclature, 53. Terminology, 53.

CHAPTER IX.

Facts of Causation and Facts of Succession . . .55
Causation defined, 55. Count Rumford's experiment, 56. Rumford's
experiment discussed, 59. Energetic cause, 60. Conditional cause, 61.
Material cause^ 61. Volitional cause, 62. Lotze on the authority of

Contents. vii

PAGE

causal law, 63. Things may cause events, 64. Events may cause events,
65. Historical cause, 66. Events and states, 67. Occasional causes, 68.
Incident in the life of Dr. Darwin, 69. Formal cause and final cause, 70.
Negative cause, 70. Summing up of discussion of causation, 71. Do
like causes produce like effects ? 72. Facts of succession not ultimate, 72.

CHAPTER X.

Mr. Mill's Doctrine of Causation 75

Mill's eminence, 75. Notion of cause the root of the whole theory of
induction, 75. Uniformity of nature not the immediate major premise,
76. Deiinition of cause, ']']. All conditions equal, 78. Cause the sum
total of conditions, 80. Cause and effect not necessarily successive, 83.
Succession not between single antecedents and consequents, 85. Cause
the total of immediately preceding conditions, 85. Unconditionalness, 85.
Night not the cause of day, 86. The will under the law of causation, %"].

CHAPTER XL

Canons for Isolating Facts of Causation . . . .91

Comprehensive cause defined, 91. Mechanical isolation, 92. Isolation
in thought, 93. Canon for Test of Difference, 93. Empirical cause, 93.
Four cases under the canon, 94. Expression of cases in symbols, 97.
Use of the facts isolated, in making inductions, 98. Canon for Test of
Agreement, 99. Schiller on moral decline and aesthetic culture, 100. Ex-
pression of cases in symbols, loi. The Plurality of Causes, 102.

CHAPTER Xn.

Mr. Mill's Four Experimental Methods .... 103

The methods are fundamentally two, 103. The five canons, 104. The
method of residues the same as the method of difference, 106. All the
methods deductive, 106. Correction of instances, 107. The term " experi-
mental," 107. Vagueness of terms and results, 107. Failure to hold fast
the idea of sequence, 108. Investigation of crystallization, 108. Is the
noun or the verb the cause ? 109. The joint method of agreement and
difference an illusion, 109, Investigation of the cause of dew, no. Method
of concomitant variations not distinct, iii. Mill exaggerates the im-
portance of the methods, 112. Difference between ancient and modern
thought, 113.

viii Contents.

CHAPTER XIII.

PAGE

Hypothesis 115

Hypothesis defined, 115. Theory, 115. No explanation of uniform-
ities, 116. The " laws of. nature," 116. Incident in the life of Darwin, 117.
Rules for legitimacy of hypotheses, 118. Vera causa, 118. Mill's defini-
tion, 119. Discovery of planet Neptune, 120, Darwin's theory of coral
islands, 121. Helmholtz on forming hypotheses, 124. Whewell on the
Greek physical philosophy, 125. Davis on function of hypothesis, 126.
Value of false hypotheses, 127.

CHAPTER XIV.

Inductive Arguments 129

Analogy, 129. Bishop Butler on probability, 129. Analogy a variety
of primary induction, 130. Asa Gray on trees, 130. Robinson Crusoe,
133. The Cincinnati glacial dam, 133. Analysis of Wright's argument,
135. Verification, 136. Trials at law, 138. Testimony to observation,
139. Hume on the grounds for accepting testimony, 139. Relevancy, 142.

CHAPTER XV.

Fallacies 146

Bacon's " idols," 146. Non-observation or Prejudice, 150. Aristotle on
the skull, 151. Bacon on wooden arrows, 152. Authority, 152. Modern
teaching not dogmatic, 153. Scheiner and the. sun spots, 154. Partial

Observation, or Neglect of Negative Instances, 154. Example from

Brachet, 154. The Greek aorist, 156. The definition of a verb, 157.
Signs of the weather, 157. Malobservation, 158. Mistake in Area, 159.
"Adjacent cases," 159. The Indian prince, 159. Hume's mistake, 160.
The law of motion, 160. Mistake in Isolation, 160, Experiment of Van
Helmont, 161. Post hoc, ergo propter hoc, 162. Mutuality of Cause and
Effect, 163.

CHAPTER XVI.

The Work of Bacon 165

Lord Macaulay on Bacon, 165. Reid's opinion, 165. Bacon's claim,
166. Minto's estimate, 167. Mill's criticism, 168.

INDUCTIVE LOGIC

CHAPTER I.
INTRODUCTORY.

Inductive Logic is the Science of the Discovery of
Facts not directly observable. A few facts are known
to us without discovery. Such are our personal iden-
tity, moral freedom, and obligation. Certain truths
also are recognized by the mind as certain as soon as
they are suggested. Evidence is not required to
establish them, nor can it in any w£.y confirm them.
Of these are the axioms of Mathematics and the
canons of Deductive Logic. This furniture is the
same for all minds and the possession of it is what
makes thinking possible. Only all minds do not with
equal clearness analyze their own operations, and the
most lack the patience, concentration, and strength
to follow admitted principles to their ultimate con-
sequences.

Whole sciences have been built up by simply
developing the necessary implications of the few
simple but universal truths intuitively perceived by
every mind. Deductive Logic and Mathematics are
examples. One peculiarity of them is that they are
the same for all minds, and that when the terms used

2 Inductive Logic.

are precisely understood there is no difference of
opinion possible among sane men. These are pure
sciences; they do not depend upon the actual exist-
ence of any person or thing, but we know that whatever
does exist, necessarily conforms to them. If numbers
or quantities of objects exist anywhere, they are in
mathematical relations; if correct thinking upon any
subject is done by rational beings anywhere, it i& done
according to the rules of deductive logic.

But the great bulk of our knowledge does not come
to us by intuition. Beyond the few facts and truths
with which the mind starts, lies the whole universe of
reality, which we can know only through observation.
Over against the pure sciences stand the applied sci-
ences. The main value of the pure sciences is in the
fact that they furnish the principles for constructing
the applied sciences. The latter have no new formal
principles of their own.

This last point is of supreme importance for the
purpose now in hand. It has been extensively sup-
posed that the field of thinking was divided into two
kingdoms, ruled by two sovereigns. Deductive and
Inductive Logic, under dissimilar constitutions, and
that what was bad law in one kingdom might be good
law in the other. It has been assumed that sometimes
two thoughts which could show no right to union in
the domain of Deduction could cross the border and,
by a sort of Gretna Green marriage, make a synthesis
in the kingdom of Induction. A little reflection should
have shown all this to be a huge mistake. The canons
of deductive logic are the universal laws of thought.
They are invariably true, if ever true. The only

Introductory. 3

ground upon which we assent to any principle in
deductive logic is our instant perception of its neces-
sary and universal validity. If so, we cannot step into
another province and escape its force. The limits of
its domain are the same as those of correct thinking.

Deductive and Inductive Logic are not two sister
sciences which divide the empire of thinking between
them. They are not mutually exclusive ; one does not
stop where the other begins. One is not the inverse
of the other. One does not proceed from generals to
particulars, while the other moves from particulars to
generals. It is not true that one infers from the
known to the known, while the other infers from the
known to the unknown. It is not true that one is
rigorously required to draw conclusions no wider than
its premises, while the other is warranted in concluding
the universal from a part. Many such assertions have
been made by philosophers, but it is obvious without
discussion that, if there is any truth in deductive logic,
all these assertions are false ; for deductive logic sways
a universal scepter or none. There can be no legiti-
mate thinking except according to its laws. Inductive
Logic is simply deductive logic regulating our reason-
ing upon our observations of the phenomena of the
universe. It is deductive logic applied in the realm of
reality. Whenever in our thinking a proposition is
introduced the truth of which depends not upon its
harmony with a previous admission, but directly upon
observation, there our reasoning becomes Inductive.
There is no new way of inferring peculiar to Induction.
Deductive logic deals with the mutual harmony of
propositions. Inductive logic deals with the harmony

4 Inductive Logic.

between propositions and facts. No reasoning of any
kind, deductive or inductive, can ever carry knowledge
a step forward into the unknown, or do anything more
than unfold what is contained in the premises.

We can learn the unknown only by observation ; we
can reason upon our observations in no other way than
deductively ; for that is the only way men can reason
at all. The rational action of the mind upon the data
of observation is called Induction.

In defining Inductive Logic as the science of the
Discovery of Facts we use the word discovery in the
strictest sense, as meaning the ascertainment of the
absolutely unknown.

To quote from Archbishop Whately : — -

" There certainly are two kinds of ' New Truth ' and of
' Discovery,' if we take those words in the widest sense in which
they are ever used. First, such truths as were, before they were
discovered, absolutely unknown, being not implied in anything we
previously knew, though we might perhaps suspect them as
probable ; such are all matters of fact strictly so-called, when
first made known to one who had not any such previous knowl-
edge as would enable him to ascertain them a priori^ /.<?., by
reasoning ; as, if we inform a man that we have a colony at
Botany Bay ; or that the earth is such a distance from the sun ;
or that platina is heavier than gold. The communication of this
kind of knowledge is most usually and most strictly called infor-
mation; we gain it from observation^ and from testi7nony j no
i7iere internal ^vor kings of our own minds (except when the mind
itself is the very object to be observed), or mere discussions in
words will make these known to us ; though there is great room
for sagacity in Judging what testimony to admits and forming
conjectures that may lead \.o profitable observation^ and to experi-
ments with a view to it. The other class of Discoveries is of a
very different nature. That which may be elicited by Reasoning,

Introductory. 5

and consequently is implied in that which we already know, we
assent to on that ground, and not from observation or testimony :
to take a geometrical truth upon trust, or to attempt to ascertain
it by observation, would betray a total ignorance of the Science." ^

In the following treatise we shall first inquire what
is meant by "a fact," and shall then follow as exactly
as possible the processes of mind by which facts are
ascertained. The several fallacies to which the unwary
are exposed will receive a large share of attention.
The points to be considered will require hard thinking,
but if any advance in clearness is made, the labor will
be well repaid ; for inductive thinking is the largest
part of the work of life.

1 Whately's Logic, p. 216.

CHAPTER II.
FACTS.

Since Inductive Logic is the science of the Dis-
covery of Facts, it is necessary to consider at the
outset what is meant by a fact. The human mind
finds itself in a universe of phenomena. Through the
senses it has perceptions of an external world, and
through consciousness it knows its own modifications.
Through these channels alone can the mind advance in
knowledge of realities. Whatever has real existence
is a fact. It may be a substance, an energy, a quality,
an action, a state, or only some relation of substances,
energies, qualities, actions, or states, but if it be
perceived by the mind it is a fact. A dragon is not a
fact, because it is not perceived; but the notion of a
dragon is a fact, for that is an action of the mind of
which I am conscious. The sun is a fact, the continent
of America is a fact; the yellow color of gold, the
attraction of a magnet, the likeness of two peas, are
facts.

For the purposes of induction, facts may be classi-
fied as substantive facts and facts of relation. A
substantive fact is a phenomenon considered apart, as
independently existing. The yellowness of gold, the
weight of gold, the malleability of gold, are substantive
facts. A fact of relation connects in some way two
substantive facts. That malleability and yellowness
coexist in gold is a fact of relation.

Facts. J

Facts of relation are of three kinds: Facts of
Resemblance, Facts of Coexistence, and Facts of
Causation. Facts of Succession are often named
among the ultimate kinds, but, as we shall see later,
they are dependent upon simpler facts of causation.

One of the first lessons received by a child when it
begins, as we say, to notice, is that there are many
things in the world which resemble one another.
Often the resemblance is so complete that the several
phenomena seem but repetitions of the same thing.
Thus from the observation of individual facts we pass
through the perception of resemblances to the forma-
tion of a general concept. Common nouns are but the
names of indefinite numbers of facts that resemble one
another. The possibility of language arises from the
constant repetition of similar things for which the
same words will do.

It is also observed that there are certain more or less
constant groups of substantive facts. We repeatedly
find yellowness, sweetness, roundness, etc., coexisting ;
and to this assemblage of phenomena we give the
name orange. We find yellowness, malleability, spe-
cific gravity 19.32, etc., coexisting, and we call this
group of coexistences gold.

It is observed that when certain substantive facts or
groups of substantive facts are in a certain collocation,
a reaction occurs between them and that this is often
attended by a change in one or more of the facts or
groups. The relation between facts or groups of facts
and their reactions, as well as the relation between any
fact or group of facts and itself in a new form, is called
Causation.

8 Inductive Logic.

Further it is observed that certain substantive facts
appear in succession; thus, after a ball is struck, we
see it move; after a bell is swung, we hear a sound;
after we touch fire, a smart follows. The relation by
which an antecedent fact is linked to a consequent one
we call Succession. Careful attention to the facts of
succession is a large part of the work of science, since
it is in most cases impossible to bring immediately
into existence the phenomena which we desire; we
produce them indirectly by producing their antecedents.

We do not know why certain simple facts coexist or
why certain phenomena resemble each other or why
certain things react as they do. These are ultimate
facts of the Universe. There is no law of thought
necessitating them; consequently they belong wholly
to the domain of Induction. That the most refrangible
rays of light have a violet color, and that the least
refrangible rays have a red color, are facts for which no
one expects ever to know a reason. Science makes
no progress in this direction.

CHAPTER III.

OBSERVATION.

The first step in the discovery of facts is always
Observation. In order to know what is passing in
our own minds or in the external world, we must give
attention. Each act of attention is called an Observation.
To quote the words of Bacon : " Man, being the servant
and interpreter of Nature, can do and understand so
much, and so much only, as he has observed in fact or
in thought of the course of nature : beyond this he
neither knows anything nor can do anything." ^ The
five senses report to the mind the world of matter and
force ; consciousness interprets to the thinking subject
his own activities. Perception and consciousness sup-
ply the materials out of which the structure of Inductive
Science is built up. But thought can build nothing
without the use of those primary facts and necessary
truths which are known by intuition without the process
of discovery. There is nothing peculiar in any process
of inference in inductive investigation ; for by the
nature of the mind there can be but one mode of
inference, namely that of deduction. The element of
observation is the essential characteristic of Induction.
Any syllogism is inductive in which one of the premises
formulates the observation of some fact. The great
work of Bacon was just this, that he with singular

1 Works, vol. viii, p. 67.

lO IndiLctive Logic.

clearness, persuasiveness, and charm of language called
mankind to patient observation of Nature.

A distinction is sometimes made between Observa-
tion and Experiment. Dr. Fowler says : —

" To observe is to watch with attention phenomena as they
occur ; to experiment (or, to adopt more ordinary language, to per-
form ail experiineiif) is not only to observe, but also to place the
phenomena under pecuHar circumstances, as a preHminary to
observation. Thus every experiment implies an observation, but
it also implies something more. In an experiment, I arrange or
create the circumstances under which I wish to make my observa-
tion. Thus, if two bodies are falling to the ground, and I attend
to the phenomenon, I am said to observe it, but if I place the
bodies under the exhausted receiver of an air-pump, or cause them
to be dropped under any special circumstances whatever, I may-
be said not only to make an observation, but also to perform an
experiment. Bacon has not inaptly compared experiment with the
torture of witnesses. Mr. Mill distinguishes between the two
processes, by saying that in observation we find our instance in
nature, in experiment we make it, by an artificial arrangement of
circumstances."^

All this is very clear: indeed, it is so clear that one
is surprised that the discussion of experiments did not
come up in connection with a classification of instances,
as natural and artificial. The fact that we can make
instances artificially is of great importance in the
progress of science ; but it is not properly the basis of
any distinction regarding the act of observation, which
is always the same whatever the origin of the instance.
There is no more contrast between an observation and
an artificial instance than there is between an observa-
tion and a natural instance. Nor is the difference

1 Inductive Logic, p. 40.

Observation. 1 1

between natural and artificial instances, that is, between
experiments and instances which are not experiments,
always clearly traceable. All of the arrangements of
human life and society are artificial ; we learn from
them to our cost, and often, in consequence, change our
methods. Popular government is frequently spoken of
as still an experiment ; the construction of our armored
battle ships is experimental. Yet instances of this
kind are not arranged for the sake of learning from
them, although with the expectation of learning, and
improving.

The primary rule for any inductive thinking is to
make sure of the observations. Starting with preju-
dices, guesses, or inferences, the truth never can be
reached. Nothing but observation can establish a
hitherto unknown fact. The explanation of the slow
advance of science in ancient and mediaeval times may
be found mainly in the neglect of this simple rule. In
spite of many errors in methods of thinking, the men
of those times would have discovered a vast body of
facts, if they had only given attention to them.

But the making of a precise and trustworthy observa-
tion is by no means the easy thing which at first it
seems to be. Very much of what passes for observa-
tion is merely mistaken inference. An amusing illus-
tration occurs in Charles Darwin's recollections of his
father : —

" He himself never drank a drop of any alcoholic fluid. This
remark reminds me of a case showing how a witness under the
most favorable circumstances may be utterly mistaken. A gentle-
man-farmer was strongly urged by my father not to drink, and
was encouraged by being told that he himself never touched

12 IndiLctive Losric

spirituous liquor. Whereupon the gentleman said, ' Come, come,
Doctor, this won't do — though it is very kind of you to say so for
my sake — for I know that you take a very large glass of hot gin
and water every evening after your dinner.' So my father asked
him how he knew this. The man answered, ' My cook was your
kitchen-maid for two or three years, and she saw the butler every
day prepare and take to you the gin and water.' The explanation
was that my father had the odd habit of drinking hot water in a
very tall and large glass after his dinner ; and the butler used first
to put some cold water in the glass, which the girl mistook for gin,
and then filled it up with boiling water from the kitchen boiler." i

To quote from Dr. Fowler : —

" That which is strictly matter of perception does not admit of
being called in question ; it is the ultimate basis of all our reason-
ing, and, if we are to repose any confidence whatever in the exercise
of our faculties, must be taken for granted. But there are few
of our perceptions, even of those which to the unphilosophical
observer appear to be the simplest, which are not inextricably
blended with inference. Thus, as is well known to every student
of psychology, in what are familiarly called the perceptions of
distance and of form, the only perception proper is that of the
various tints of color acting on the retina of the eye, and it is by
a combination of this with perceptions of touch, and the muscular
sense, that the mind gains its power of determining form and
distance. Now, a judgment of this kind, which is really due to
inference, is, especially by the uneducated and unreflecting, per-
petually mistaken for that which is due to direct observation ;
and thus what is really only an inference from facts is often
emphatically asserted to be itself a matter of fact." ^

To quote from Mr. Mill : —

" One of the most celebrated examples of a universal error
produced by mistaking an inference for the direct evidence of the
senses, was the resistance made, on the ground of common sense,

^ Life and Letters, p. 15. ^ Inductive Logic, p. 273.

Observation. • 13

to the Copernican system. People fancied that they saw the sun
rise and set, the stars revolve in circles round the pole. We know
that they saw no such thing ; what they really saw was a set of
appearances, equally reconcilable with the theory they held and
with a totally different one. It seems strange that such an instance
as this of the testimony of the senses pleaded with the most entire
conviction in favor of something which was a mere inference of
the judgment, and, as it turned out, a false inference, should not
have opened the eyes of the bigots of common sense, and inspired
them with a more modest distrust of the competency of mere
ignorance to judge the conclusions of cultivated thought.

"In proportion to any person's deficiency of knowledge and
mental cultivation is, generally, his inability to discriminate between
his inferences and the perceptions on which they were grounded.
Many a marvelous tale, many a scandalous anecdote, owes its
origin to this incapacity. The narrator relates, not what he saw
or heard, but the impression which he derived from what he saw
or heard, and of which perhaps the greater part consisted of
inference, though the whole is related not as inference but as
matter of fact. The difficulty of inducing witnesses to restrain
within any moderate limits the intermixture of their inferences
with the narrative of their perceptions, is well known to experienced
cross-examiners ; and still more is this the case when ignorant
persons attempt to describe any natural phenomenon. " The
simplest narrative,' says Dugald Stewart, 'of the most illiterate
observer involves more or less of hypothesis ; nay, in general, it
will be found that, in proportion to his ignorance, the greater is
the number of conjectural principles involved in his statements.
A village apothecary (and, if possible, in a still greater degree, an
experienced nurse) is seldom able to describe the plainest case,
without employing a phraseology of which every word is a theory:
whereas a simple and genuine specification of the phenomena
which mark a particular disease, a specification unsophisticated
by fancy, or by preconceived opinions, may be regarded as
unequivocal evidence of a mind trained by long and successful
study to the most difficult of all arts, that of the faithful interpreta-
tion of nature.' " ^

1 Logic, p. 545.

CHAPTER IV.

PRIMARY INDUCTIONS.

An Induction is a generalization, or an inference,
based upon propositions that state observed facts. The
truth inferred may be general or particular, but it must
be one which we cannot perceive in a single act of
observation. When we know the existence of anything
by simply attending to it, we do not say that we know
it inductively ': we know it directly. The word Induc-
tion is applied both to the proposition enunciated and
to the process of mind by which that proposition is
reached. That "all men are mortal," I know by induc-
tion, and the truth is itself an induction.

Inductions are based either wholly upon observations,
in which case we call them Pure Inductions ; or they
are based partly upon observation and partly upon
intuitively known truth, in which case we call them
Mixed Inductions. Pure inductions are either Com-
plete or Incomplete, according as we have or have not
observed all the facts included in the statement. They
are either Primary or Secondary, according as they
are made directly by generalizing a number of observa-
tions, or indirectly by combining syllogistically a single
new observation with a previous induction. These
distinctions will become clear as we advance. The
present chapter deals with Primary Inductions.

It soon becomes plain to every child, when he begins
to observe the world, that there is an existing order of

Primary hiductions. 15

things. It is perfectly easy to conceive of a world in
which every object should be unique and every event a
surprising novelty. Such a world would contradict no
necessity of thought, although it would be hopelessly
bewildering. But such is not our world. The child's
earliest impression is of a certain permanence and uni-
formity in its environment. The same objects and
experiences remain or recur.

This conviction of an existing order finds expression
in language. The present tense in grammar does not
denote a mere moment separating the past and the
future ; it denotes a considerable and indefinite expanse
of time. Such a proverb as " The burnt child shuns
the fire " is stated in the present tense, as formulating
a fact of the existing order.

That experience falls largely into lines of uniformity
is early perceived. The child learns that there are
things called apples which are round and red and good
to eat, and that there are things called cats which have
soft fur and long tails and sharp claws, and that these
things are liable to scratch. The profoundest question
in the whole science of inductive logic is : How are
these generalizations reached t How can we ever dis-
cover that we are upon the line of a uniformity } But
this is really only a sort of metaphysical puzzle, like
the question of the possibility of motion. The exist-
ence of lines of uniformity is every moment forced
upon our observation, and the fact that they do extend
is equally conspicuous.

A Primary Induction is the statement of an observed
uniformity. Do we reach it by any process of infer-
ence } Philosophers have thought so. There is thought

1 6 Inductive Lozic.

to be here a new and peculiar kind of inference of
which deductive logic knows nothing. Professor Davis
says : " Induction is an immediate synthetic inference
generalizing from and beyond experience." ^ But this
does not appear to be a correct analysis. When there
is an inference we necessarily look about for proposi-
tions which can be syllogistically combined. Professor
Davis claims that we intuitively know the Uniformity
of Nature, and he unconsciously makes this his major
premise. But the uniformity of nature can be known
and defined only inductively, not intuitively. It is a
discovery of induction, not the basis of it.

No : if there is a permanent or recurring fact in
nature, we ascertain it simply by generalization, not by
inference.

How do we know that the mill is standing by the
river t We cannot be looking at it all of the time.
Having seen it a hundred or a thousand times we have
come to believe in its permanence. How do we know
that the water is flowing over the mill-dam } We have
seen it often and have come to' think it continuous.
Here is a permanent fact — the mill, and a uniformity
— the flow of the water ; how do we come to feel
assured of them } Not by any process of inference, but
simply by generalization. We have not reasoned about
the future or the unknown, but about the present and
the known. Whether the world will come to an end
to-night, and the river and the mill be annihilated, we
cannot predict from our observations upon them ; all
that we know is that this permanence — the mill, and
this uniformity — the flow of the stream, are facts of

1 Inductive Logic, p. 6.

Primary Inductions. ij

the existing order ; and since it would be irrational to
act, without evidence, upon the supposition of the
cessation of the existing order, we keep on carrying
grist to the mill.

A primary induction does not rest upon a process of
inference any more than does our belief in any per-
manent fact. That the cliffs of England are white is
a permanent fact ; that the crows of England are black
is a uniformity. We cannot be looking at the cliffs all
the time, and we cannot examine all the crows ; but
having looked at the cliffs frequently, and having seen
a large number of crows, we rest in the assurance that
we know the existing order. Should we wake up some
morning and find the cliffs blackened, we should simply
recognize that the order had changed. Should we find
in visiting a remote part of the kingdom a flock of
white crows, we should simply observe that we had
passed beyond the former area of observation. If our
expectation of finding the cliffs white and the crows
black at the next observation rested upon any logical
necessity, our not finding them so would require a doubt
of our own sanity.

The suggestion has been made that we base our
belief in the truth of a primary induction upon our
faith in the veracity of God. But surely such an induc-
tion as that " the Cretans are always liars " cannot be
based upon the veracity of God ; it rests merely upon
observation of the uniform mendacity of those depraved
people.

The sort of induction we are now describing has been
known, since Bacon's time, as Inductio per Enume-
rationem Simplicem, Induction by Simple Count. "It

1 8 Inductive Logic.

consists in ascribing the character of general truths to
all propositions which are true in every instance that
we happen to know of." Mr. Mill's attitude toward
such inductions in the first edition of his Logic was
curious. Although holding that the uniformity of
Nature, the law of Causation, and the axioms of Mathe-
matics are established only in this way, he yet inclined
to deny to the process even the name of induction. He
said : " This is the kind of induction, if it deserves the
name, which is natural to the mind when unaccustomed
to scientific methods." Later Mr. Mill omitted the
clause "if it deserves the name"; but his disparaging
tone continued and infected logical writers. Thus,
Dr. Fowler says : —

" But not only is the htductio per Enuinerationem Sijnplicem
the mode of generalization natural to immature and uninstructed
minds ; it is the method which, till the time of Bacon, or at least
till the era of those great discoveries which shortly preceded the
time of Bacon, was almost universal." " When men first begin
to argue from their experience of the past to their expectation of
the future, or from the observation of what immediately surrounds
them to the properties of distant objects, they seem naturally to
fall into this unscientific and unreflective mode of reasoning." ^

Bacon himself seems responsible for this sneer ; he
says : —

" Inductio quae procedit per enumerationem simplicem, res
pueriHs est, et precario concludit, et periculo exponitur ab instantia
contradictoria, et plerumque secundum pauciora quam par est, et
his tantum modo quae praesto sunt pronunciat." ^

Still there remains an inconsistency in Mr. Mill's
doctrine ; for he says most justly : —

1 hiductive Logic, pp. 280, 281. 2 JSfovum Orgamim, lib. i, aph. cv.

Primary IndiLctions. 19

" Experience must be consulted in order to learn from it under
what circumstances arguments from it will be valid. We have no
ulterior test to which we subject experience in general ; but we
make experience its own test. Experience testifies, that among
the uniformities which it exhibits or seems to exhibit, some are
more to be relied on than others ; and uniformity, therefore, may-
be presumed from any given number of instances, with a greater
degree of assurance, in proportion as the case belongs to a class
in which the uniformities have hitherto been found more uniform.
This mode of correcting one generalization by another, a narrower
generalization by a wider, which common sense suggests and
adopts in practice, is the real type of scientific induction." ^

The truth could not be better set forth than in the
foregoing accurate and discriminating statement ; after
all, the "real type of scientific induction" is merely an
indiictio per enumerationeni simplicem, carefully made.

Experience gives us not only uniformities, but uni-
formities among uniformities. Not only does this ox
uniformly chew the cud, but all oxen uniformly chew
the cud, and all other sorts of animals with similar
structure uniformly chew the cud. Not only does this
piece of lead maintain a uniform specific gravity of
1 1.4, but there is a uniformity in specific gravity among
all pieces of lead, and, moreover, every different sub-
stance maintains a uniform specific gravity. What we
call the "Principle of the Uniformity of Nature" is
merely the wide primary induction that the various
limited uniformities of nature persist. There is no
other sense in which nature is uniform. It is not
meant, of course, that every object is like every other
object, and every event like every other event.

1 Logic, p. 232.

20 Inductive Logic.

" Every person's consciousness assures him that he does not
always expect uniformity in the course of events ; he does not
always beUeve that the unknown will be similar to the known,
that the future will resemble the past. Nobody believes that the
succession of rain and fine weather will be the same in every
future year as in the present. Nobody expects to have the same
dreams repeated every night. On the contrary everybody mentions
it as something extraordinary, if the course of nature is constant,
and resembles itself in these particulars. To look for constancy
where constancy is not to be expected, as for instance that a day
which has once brought good fortune will always be a fortunate
day, is justly accounted superstition." ^

The assurance with which a primary induction is
held, depends upon the number of instances from which
it is generalized. If the number is small, the assurance
is imperfect : if the number of instances is practically
infinite, the assurance is practically complete. Belief
shades thus from faint presumption, by imperceptible
increments, into positiveness. When at last we have
examined all the instances, the induction is complete
and we know. To quote Mr. Mill: —

" Induction by simple enumeration — ■ in other words, generali-
zation of an observed fact from the mere absence of any known
instance to the contrary — affords in general a precarious and
unsafe ground of assurance ; for such generalizations are inces-
santly discovered, on further experience, to be false. Still, how-
ever, it affords some assurance, sufficient, in many cases, for the
ordinary guidance of conduct. It would be absurd to say, that
the generahzations arrived at by mankind in the outset of their
experience, such as these — food nourishes, fire burns, water
drowns, — were unworthy of reliance. There is a scale of trust-
worthiness in the results of the original unscientific induction; and
on this diversity (as observed in the fourth chapter of the present

1 Mill's Logic, p. 226.

Primary Inductions. 21

book) depend the rules for the improvement of the process. The
improvement consists in correcting one of these inartificial gener-
alizations by means of another. As has been already pointed out,
this is all that art can do. To test a generalization, by showing
that it follows from or conflicts with some stronger induction,
some generalization resting on a broader foundation of experience,
is the beginning and end of the logic of induction." ^

Quite a different view from the foregoing has, how-
ever, been often taken. The name induction has been
denied to the generalization of experience, and has
been reserved exclusively for statements in regard to
the unobserved. Professor Bain speaks as follows : —

" Induction is the arriving at General Propositions, by m.eans of
Observation or Fact.

" In an induction there are three essentials: (i) the result must
be a proposition — an affirmation of concurrence or non-concur-
rence — as opposed to a Notion; (2) the Proposition must be
general^ or applicable to all cases of a given kind; (3) the method
must be an appeal to observation of fact.

" The Propositions established by induction are general. A
single individual concurrence, as ^ the wind is shaking the tree,' is
in its statement a proposition, but not an induction. On such
individual statements we base inductions, but one is not enough.
If the coincidence recurs, we mark the recurrence; we are affected
by the shock or flash of identity, a very important step in our
knowledge. If, pursuing the suggestion, we remark that as often
as the wind is high, the trees are shaken; that the two things
have concurred within the whole course of our observation; that
the same concurrence has been uniform in the observation of all
other persons whose experience we have been informed of, — we
are then entitled to make a still wider sweep, and to say, ' every
time that a high wind has been observed, a waving of the trees
has also been observed.'

" Still, with all this multitude and uniformity of observations,

1 Logic, p. 401.

22 Inductive Logic.

there is no proper Induction. What then remains ? The answer
is, the extension of the concurrence from the observed to the
unobserved cases — to \\\% future which has not yet come within
observation, to the past before observation began, to the remote
where there has been no access to observe. This is the leap, the
hazard of Induction, which is necessary to complete the process.
Without this leap our facts are barren; they teach us what has
been, after the event ; whereas we want knowledge that shall
instruct us before the event, that shall impart v/hat we have no
means of observing. A complete induction, then, is a generaliza-
tion that shall express what is conjoined everywhere, and at all
times, superseding forever the labor of fresh observation.

" We thus contrast Induction with that species of ' Induction
improperly so-called,' where a general statement merely sums up
the observed particulars.

^' If, after observing that each one of the planets shines by the
sun's light, we affirm that ' all the planets shine by the sun's light,'
we make a general proposition to appearance, but it falls short of
an induction in the full sense of the term. The general statement
is merely another way of expressing the particulars; it does not
advance beyond them. But without such advance there is no real
inference, no march of information, no addition to our knowledge.
Induction is the instrument of multiplying and extending knowl-
edge; it teaches us how, from a few facts observed, to affirm a
great many that have not been observed. If, from the observa-
tion of the planets now discovered, we make an assertion respect-
ing all that have yet to be discovered, we make the leap implied
in real or inductive inference. If the assertion had been made
when only six planets were known, actual observation would have
been the guarantee for those six, induction for the remaining hun-
dred or upwards.

" The sole method of attaining Inductive truths being the
observation and comparison of particulars, the sole evidence for
such truths is Universal Agreement.

" A permanent or uniform concurrence can be established, in
the last resort, only by the observation of its uniformity. That
unsupported bodies fall to the ground, is a conjunction suggested
by the observation of mankind, and proved by the unanimity of all

Primmy Inductions. 23

observers in all times and places. What is found true, wherever
we have been able to carry our observations, is to be accepted as
universally true, until exceptions are discovered.

" Through this method alone — of Universal Agreement in
detail — can our most general and fundamental truths be dis-
covered and proved. It is the only proper inductive jnethodP ^

This account of induction cannot be consistently ac-
cepted. The Professor suggests no criterion by which
one may know when he is justified in taking the hazard
of a leap in the dark and making an induction. He
does not say how many instances must be observed
before the leap is warranted. If only that part of a
generalization which refers to the unobserved is
"induction proper," and if "the only proper inductive
method is the observation of particulars," and if
"the sole evidence for such truths is universal agree-
ment,"— it is impossible to see how we can have any
induction at all. If " a permanent or uniform concur-
rence can be established in the last resort, only by the
observation of its uniformity," then it cannot be estab-
lished by what Professor Bain calls induction ; for
"proper induction" deals only with the unobserved.
The puzzle here is simply what grows out of the
mind's necessary assumption of the continuity of the
existing order. Of course no one can prove the per-
manence of a thing by observing it every moment.
How do I know that the sun does not go out of
existence whenever I cease to look at it } The answer
is, that having no reason in experience to think that the
existing order depends upon my attention, I must assume
that it does not. The truth is that if, after observing

1 Logic : Deductive and Inductive, pp. 231, 232, 237.

24 Inductive Logic.

that each of the planets shines by the sun's light, we
affirm that "all the planets shine by the sun's light,"
we take the " hazard " of the continuance of the existing
order, for we are not at this moment observing them.

When we say, Salt preserves meat, we are not,
according to Professor Bain, uttering an induction;
because the preserved meat is now under our eyes;
it is only when we say that salt will preserve meat, or
that salt has preserved meat (referring strictly to the
unobsei'ved cases in the past), that an induction is made:
yet this can be established only by " the unanimity of
all observers," which it is manifestly impossible to
ascertain, and if it could be ascertained, the assertion
would at once cease to be an induction (since no longer
referring to the unobserved and making no addition to
knowledge) : it would be a mere generalization, an
"induction improperly so-called."

It would be impossible to make a catalogue of all of
the primary inductions held by the mind of a single
person. They refer to every object and undergo
constant revision and extension. They are not always,
nor even usually, in the form of universal truths. That
three-fifths of the wheat in the state is bad, and that on
the average ten men in a thousand of a certain class
die every year, are primary inductions. By combination
of inductions of small extent, wider ones are. made, and
a steady advance in generality is the result. It is the
peculiar glory of modern science to have formulated
such grand inductions as the law of Inertia, that is,
that every body continues in its state of rest or motion
unless acted upon ; the law of the persistence of
energy; the lav/ of the persistence of matter; the law

Primary Inductions. 25

that the will can transform some of the energy of the
body. These laws generalized into a higher induction
give us the great law of Causation; namely, that if any
change occurs in things, the matter, the force, and the
will concerned, can be found among previously existing
things. Another generalization is, that as far as man
can explore, the same order is found existing. So far
as the sun and stars can be observed, they conform to
the one existing order.

How long the existing order will continue, we cannot,
in any proper sense, be said to know. Reasoning can-
not make any addition to knowledge. Up to the year
79 A.D., the volcano of Vesuvius had had, within the
memory of man, no eruption. Experience seemed to
have demonstrated that it was safe to live upon its
slopes ; but the eruption came and proved the contrary.
Manifestly, those uniformities which depend upon the
co-operation of a number of causes are less stable than
those which are simpler. Nothing is simpler than the
law of gravitation; hence such a uniformity as the
rising and setting of the sun is relied upon with vastly
more faith than is the quiescence of a volcano. But
that is only a matter of degree.

Mr. Mill has made a distinction between Empirical
Laws and Ultimate Laws. "An empirical law is an
observed uniformity, presumed to be resolvable into
simpler laws, but not yet resolved into them." The
distinction is simple enough in thought, but in practice
it is impossible to draw the line.

It may be well, in closing this chapter, to say a few
words upon the curious popular misunderstanding of
the maxim that "The exception proves the rule."

26 Inductive Logic.

When one has laid down with positiveness some sup-
posed general principle, and his attention is called to a
fact inconsistent with it, it is not uncommon to hear
him say, rather triumphantly, " Oh, that is simply the
exception that proves the rule"; and he seems some-
how to feel better fortified in his position than before,
his generalization being now provided with a necessary
equipment. Even respectable writers fall into this
absurd mode of speaking. The fallacy consists in
taking as a principle, valid in the world of facts, what
has no sense at all except in the world of statements.
It is taken as if the finding of a black sheep were in
some way a confirmation of the generalization that all
sheep are white ; although, of course, every such case
is just so much disproof. But if some person, a law-
maker, an expert, or an authority of some sort, in mak-
ing statements, excepts a person or thing, then it may
be legitimately inferred that he assumes the rule to be
the other way. If, for example, one who lives on the
shore of Lake Erie speaks of a fine day in March with
surprise, his so speaking is equivalent to testimony that
bad weather then and there is the rule ; but a chance
visitor, luckily enjoying bright skies, would not on that
account more readily assent to the assertion that March
weather on Lake Erie is generally bad. Those who in
their youth have been compelled to learn the rules for
Latin quantity, find it most convenient to remember
them by the exceptions. Knowing that amicus is given
as one of the exceptions in its class, I have no difficulty
in recalling the rule that " Words in -icus shorten the
penult"; but this proves only the statement of the
grammarian, nothing more. In short, the word excep-

Primary hidiictions. ^ 27

Hon has two senses ; first, it means the act of excepting ;
secondly, the thing excluded ; the popular fallacy con-
sists in substituting the second for the first sense, and
in supposing that the discovery of a few words with long
i before the termination -cus makes it easier to believe
that i so situated is generally short ; when in truth the
proof is wholly in the fact that a competent authority
has declared these words to be exceptions.

CHAPTER V.
SECONDARY INDUCTIONS.

Having by the slow, and often tedious, process of
observing many particulars, established our primary
inductions, we are prepared to advance with ease and
rapidity in the making of Secondary Inductions. A
primary induction, we have learned, is a generalization
of experience, a truth established by repeated observa-
tions. A Secondary Induction is the conclusion of a
syllogism of which one premise is a primary induction,
and the other premise is the statement of an observed
fact. When, for example, it has once been admitted,
as a primary induction, that specific gravities are con-
stant, a single experiment upon a newly discovered
metal is sufficient to establish its specific gravity to the
satisfaction of the scientific world. The single observa-
tion is combined deductively with the primary induction,
thus : —

All specific gravities are constant ;

The specific gravity of this piece of Rubidium is 1.5;

Therefore, the specific gravity of Rubidium is always
1.5.

This illustration shows in an interesting manner how
induction and deduction are combined. There is dis-
covery here, but it is not reached by anything peculiar
in the method of inference ; that is simply deductive.
But each of the premises records a discovery made by
observation ; hence the syllogism is inductive. It has

Secondary Inductions. 29

been objected to such syllogisms, that the universal
proposition could not be affirmed unless we already
knew the conclusion, and that consequently there is
only an apparent, and not a real advance in knowledge.
The reply is, that no reasoning can ever make a sub-
stantial advance in knowledge ; to give knowledge is
the function of intuition and observation alone. Rea-
soning can only display explicitly what was already
involved implicitly. There is, however, in this case
what comes very near to positive discovery. It has
appeared in the last chapter that practical certainty is
reached, regarding many of the uniformities of nature,
long before all instances have been examined ; indeed,
from the very character of most uniformities, it is
impossible that all instances should be examined. We
become satisfied that all men are mortal, upon knowl-
edge of what is a very limited part of the experience of
the race. When, therefore, it is observed that Socrates
is a man, the conclusion that he is mortal comes very
near to being a discovery. The fact that Socrates is a
man is a discovery of observation ; Socrates might be
the name of a dog or of a ship. This premise brings
into the syllogism an advance in knowledge.

In every-day thinking, primary and secondary induc-
tions are constantly mingled, and almost all of our
generalizations partake of the nature of both, or are
proved in both ways. There is, for instance, a perpet-
ually accumulating mass of experience that lead is
heavy, that aluminum is light, and so on. Independ-
ently of anything else, a primary induction can be
made regarding each one of the metals. But at the
same time the broader primary induction that specific

30 Inductive Logic.

gravities are constant is receiving perpetual confirma-
tion, so that each ■ single experience with lead or
aluminum abundantly warrants a secondary induction
covering the whole existing amount of that metal.

After observing a thousand uniformities, every one
perceives that objects and events in this world run in
lines of similarity ; a strong presumption, therefore,
arises that any given object is only one of a class.
Finding several similar things, we combine the observa-
tion with the previously established generalization that
several similarities indicate the line of a uniformity, and
make an induction accordingly. This is what Dr. Fow-
ler has called ''the mode of generalization natural to
immature and uninstructed minds"; but in truth it is
the necessary procedure of all sane minds. The imma-
turity and inexperience appear in neglecting care in
determining the exact course and limits of the lines of
uniformity.

Archbishop Whately regarded the uniformity of the
course of nature as the ultimate major premise in all
inductions. That is, he did not provide for any primary
inductions at all. But the uniformity of nature is too
vast and indefinite an induction for immediate use, even
in most cases of secondary induction. The doctrine
does not mean that all objects are alike, and all events
alike ; it only means that all particular lines of uni-
formity persist. What these lines are, must be deter-
mined simply by accumulating instances and making
generalizations. We must have observed a number of
lines of particular uniformity, before we could ascend to
the induction of the general uniformity of nature. To
quote Mr. Mill: —

Secondary Inductions. 31

" But though it is a condition of the validity of every induction
that there be uniformity in the course of nature, it is not a neces-
sary condition that the uniformity should pervade all nature. It
is enough that it pervades the particular class of phenomena to
which the induction relates. An induction concerning the motions
of the planets, or the properties of the magnet, would not be
vitiated though we were to suppose that wind and weather are the
sport of chance, provided it be assumed that astronomical and
magnetic phenomena are under the dominion of general laws.
Otherwise the early experience of mankind would have rested on a
very weak foundation ; for in the infancy of science it could not
be known that all phenomena are regular in their course." ^

The strangest fact in the history of inductive science
is that writers have never distinctly recognized and
stated the fundamental differences of the three great
classes of inductions, but have persisted in attempting
to make one comprehensive definition for all, as if the
process of induction were always precisely the same
thing. Thus Whately provides only for secondary
inductions ; Bain, only for primary ones ; Minto and
Davis, only for such secondary ones as fall under the
primary induction of causation, which is but a fraction
of the field of experience. Mr. Mill has thrown so
much light upon the whole subject, and has made so
many just discriminations, that it is all the more sur-
prising that he has not gone a step farther. He says : —

"Whatever be the most proper mode of expressing it, the
proposition that the course of nature is uniform, is the funda-
mental principle, or general axiom of Induction. It would yet be
a great error to offer this large generaHzation as any explanation
of the inductive process. On the contrary, I hold it to be itself
an instance of induction, and induction by no means of the most
obvious kind. Far from being the first induction we make, it is

1 Logic, p. 225, note.

32 Inductive Logic.

one of the last, or at all events one of those which are latest in
attaining strict philosophical accuracy. As a general maxim,
indeed, it has scarcely entered into the minds of any but philoso-
phers ; nor even by them, as we shall have many opportunities of
remarking, have its extent and limits been always very justly con-
ceived. The truth is, that this great generalization is itself founded
on prior generalizations. The obscurer laws of nature were dis-
covered by means of it, but the more obvious ones must have been
understood and assented to as general truths before it was ever
heard of. We should never have thought of affirming that all
phenomena take place according to general laws, if we had not
first arrived, in the case of a. multitude of phenomena, at some
knowledge of the laws themselves ; which could be done no other-
wise than by induction. In what sense, then, can a principle,
which is so far from being our earliest induction, be regarded as
our warrant for all the others ? In the only sense in which (as
we have already seen) the general propositions which we place at
the head of our reasonings when we throw them into syllogisms,
ever really contribute to their validity. As Archbishop Whately
remarks, every induction is a syllogism with the major premise
suppressed ; or (as I prefer expressing it) every induction may be
thrown into the form of a syllogism by supplying a major premise.
If this be actually done, the principle which we are now consider-
ing, that of the uniformity of the course of nature, will appear as
the ultimate major premise of air inductions, and will, therefore,
stand to all inductions in the relation in which, as has been shown
at so much length, the major proposition of a syllogism always
stands to the conclusion ; not contributing at all to prove it, but
being a necessary condition of its being proved ; since no conclu-
sion is proven, for which there cannot be found a true major
premise." 1

In this passage the characteristic peculiarities of Mr.
Mill's mind appear; he tells the truth most clearly, but
at the same time contradicts and obscures it. If the
uniformity of nature is a discovery of induction it cannot

1 Logic, p. 224.

Secondary Inductions. 33

be the fundamental principle of induction. We cannot
lift ourselves over the fence by our own boot-straps.
Primary inductions are but generalizations and need no
major premise; for they cannot be thrown into syllo-
gistic form. Secondary inductions have for their
major premises the particular uniformities which are
proximate. We cannot take the uniformity of nature
as a major premise, and making a single observation,
proceed at once to a secondary induction, reasoning,
This object is mortal ; But since nature is uniform ; All
objects are mortal. The uniformity of nature is a
generalization only regarding uniformities ; to use it at
all we must, by accumulating particulars, ascertain the
existence of a uniformity. And then we can reason.
All uniformities persist ; This is a uniformity ; There-
fore it will persist. The only inference that can be
drawn from the uniformity of nature is the persistence
of a newly discovered uniformity.
Professor Minto says: —

" In his antagonism to a supposed doctrine that all reasoning is
from general to particular, Mill maintained simpliciter that all
reasoning is from particulars to particulars. Now, this is true
only secundum quid, and although, in the course of his argument,
Mill introduced the necessary qualifications, the unqualified thesis
was confusing. It is perfectly true that we may infer — we can
hardly be said to reason — from observed particulars to unob-
served. We may infer, and infer correctly, from a single case.
The village matron, called in to prescribe for a neighbor's sick
child, infers that what cured her own child will cure the neigh-
bor's, and prescribes accordingly. And she may be right. But
it is also true that she may be wrong, and that no fallacy is more
common than reasoning from particulars to particulars without the
requisite precautions." ^

1 Logic, p. 266.

34 Inductive Logic.

We cannot admit that there is any such thing as
inferring, or reasoning, from one particular to another.
The village matron does not infer from her child to the
neighbor's grindstone or barn-door, and the fact that
she does not is proof that she does not take particulars
at random. Her process of thought is this : These two
particulars (the children) belong to the same natural
kind ; Things of the same natural kind are similarly
affected by the same thing ; This medicine cured my
child; Therefore, it will cure this one. The matron's
reasoning is syllogistic throughout ; if she makes an
error it is simply in observation as to whether the
medicine did cure her own child, or as to whether the
neighbor's child is in the same physical condition.
The matron proceeds from primary inductions through
particular observations to secondary inductions. The
"requisite precautions" always include attention to
these steps.

In the first edition of his Logic, Mr. Mill said: —

" The induction by which they [the mathematical axioms and
the law of causation] are established is of that kind which can
establish nothing but empirical laws; an empirical law, however,
of which the truth is exemplified at every moment of time and in
every variety of place or circumstance, has an evidence which sur-
passes that of the most rigid induction, even if the foundation of
scientific induction were not itself laid (as we have seen that it is)
in a generalization of this very description." ^

In this remarkable passage, it was assumed that only
secondary inductions are scientific inductions, and yet
it was affirmed that they are based upon the primary,

1 Page 340.

Secondary Inductions. 35

and that the primary are so firm that they would sur-
pass the secondary, were it not that the secondary,
being based upon them, must be exactly as strong. It
is true that in the eighth, the last, edition of the Logic
this passage is omitted; but the confusion of thought
still attaches to Mr. Mill's doctrine, and appears in the
books which, like Dr. Fowler's, are based upon his
earlier editions. Mr. Mill's contention amounts simply
to this, that a secondary induction made from one clear
case in combination with one of our broadest primary
inductions (say the law of causation), is far more trust-
worthy than a new primary induction made independ-
ently regarding a limited class of phenomena. And
this is undoubtedly true.

CHAPTER VI.

MIXED INDUCTIONS.

We know by intuition that if certain things are true,
certain other things are also true. When, therefore,
one of these facts of the first class has been estab-
lished by observation, one of the facts of the second
class can be established by making a syllogism, of
which one premise is known to be true by intuition,
and the other by observation; the conclusion will be a
Mixed Induction.

We know, mathematically, that if the surface of the
sea is not flat, but curved, the masts of ships must
appear before their hulls. We observe that the masts
do actually appear first. The conclusion, that the sur-
face of the sea is curved, is a mixed induction.

The nature of mixed inductions is well illustrated in
the famous discoveries of Sir Isaac Newton. We quote
from Mr. Mill : —

" Newton began by an assumption, that the force which at each
instant deflects a planet from its rectilineal course, and makes it
describe a curve round the sun, is a force tending directly towards
the sun. He then proved that, if it be so, the planet will describe,
as we know by Kepler's first law it does describe, equal areas in
equal times; and, lastly, he proved that if the force acted in any
other direction whatever, the planet would not describe equal areas
in equal times. It being thus shown that no other hypothesis
could accord with the facts, the assumption was proved; the
hypothesis became a law, established by the method of difference.
Not only did Newton ascertain by this hypothetical process the

Mixed Inductions. 37

direction of the deflecting force ; he proceeded in exactly the same
manner to ascertain the law of variation of the quantity of that
force. He assumed that the force varied inversely as the square
of the distance ; showed that from this assumption the remaining
two of Kepler's laws might be deduced; and, finally, that any
other law of variation would give results inconsistent with those
laws, and inconsistent, therefore, with the real motions of the planets,
of which Kepler's laws were known to be a correct expression." ^

That is, Newton showed mathematically that if the
planets move in a given manner, they must be affected
by a force acting toward the sun and varying inversely
as the square of the distance; Kepler had shown that
the planets do move in the given manner; the mixed
induction was therefore established that there is such a
force.

It will be seen that Mr. Mill introduces this as an
example of hypothesis, but it will also be seen that it
was wholly unnecessary for Newton to make any con-
jecture or assumption. All he had to do was to ask.
The motions being as they are observed to be, what,
mathematically, must be the direction and law of the
force } It is not necessary to form an hypothesis that
the surface of the sea is curved and then test that
hypothesis by looking at an incoming ship. All that
is necessary is to state the mathematical possibilities
and then observe the facts; the conclusion follows of
course.

We take another fine illustration from Sir John
Herschel : —

" It had been objected to the doctrine of Copernicus, that, were
it true, Venus (and, it might have been added. Mercury, as the
other inferior planet) should appear sometimes horned like the

1 Logic, p. 351.

38 Inductive Logic.

moon. To this he answered by admitting the conclusion, and
averring that, should we ever be able to see its actual shape, it
would appear so. It is easy to imagine with what force the
application would strike every mind when the telescope confirmed
this prediction, and showed the planet just as both the philosopher
and his objectors had agreed it ought to appear." ^

Having considered the three kinds of induction, we
are now ready to answer several questions proposed by
Mr. Mill: —

"In order to a better understanding of the problem which
the logician must solve if he would establish a scientific theory of
induction, let us compare a few cases of incorrect inductions with
others which are acknowledged to be legitimate. Some, we know,
which were believed for centuries to be correct, were, nevertheless,
incorrect. That all swans are white, cannot have been a good
induction, since the conclusion has turned out to be erroneous.
The experience, however, on which the conclusion rested was
genuine. From the earliest records, the testimony of all the
inhabitants of the known world was unanimous on the point. The
uniform experience of the inhabitants of the known world, agree-
ing in a common result, is not always sufficient to establish a
general conclusion. . . . When a chemist announces the existence
and properties of a newly discovered substance, if we confide in
his accuracy, we feel assured that the conclusions he has arrived
at will hold universally, although the induction be founded but on
a single instance. We do not withhold our assent, waiting for a
repetition of the experiment; or if we do, it is from a doubt
whether the one experiment was properly made, not whether, if
properly made, it would be conclusive. Here, then, is a general
law of nature, inferred without hesitation from a single instance;
an universal proposition from a singular one. Now, mark another
case and contrast it with this. Not all the instances which have
been observed since the beginning of the world, in support of the
general proposition that all crows are black, would be deemed a
sufiicient presumption of the truth of the proposition, to outweigh

1 Discoicrse on the Study of N'atural Philosophy, § 299.

Mixed Inductions. 39

the testimony of one unexceptionable witness who should affirm
that in some region of the earth not fully explored, he had caught
and examined a crow, and had found it to be gray.

" Why is a single instance, in some cases, sufficient for a com-
plete induction, while in others, myriads of concurring instances,
without a single exception known or presumed, go such a very
little way towards establishing an universal proposition? Who-
ever can answer this question knows more of the philosophy of
logic than the wisest of the ancients, and has solved the great
problem of induction." ^

Our discussion up to this point has prepared the
student to ansv^er Mr. Mill's question, and to claim the
proud distinction of " knowing more of the philosophy
of logic than the wisest of the ancients." It is plain
that when a chemist determines for the first time the
specific gravity of a new substance, rubidium, for exam-
ple, he combines this one observation deductively with
the acknowledged primary induction that chemical and
physical properties of the several natural kinds are
constant, and thus reaches at once the secondary induc-
tion, that the specific gravity of rubidium will be always
found 1.5, or whatever the determination may be.
Whenever a single instance leads to an induction, it
is a secondary induction or a mixed induction. Bacon
called such instances "crucial instances," from the
Latin crux, a finger-post ; since they point out the line
of uniformity. No single instance can give a primary
induction. In investigating the color of swans and
crows we start with the well-established primary induc-
tion that color is, in animals, an uncertain quality.
Combining this with the observation that these crows
are black, we, of course, reach no conclusion. We have,

1 Logic, p. 227.

40 Inductive Logic.

however, made a primary induction that all English
crows are black ; and this is correct. This leads us to
remark that, in making an induction, it is necessary to
define correctly the field under investigation. Having
seen a thousand Chinamen in California, we conclude
by induction that all Chinamen are, on the average,
shorter than Americans. But when we learn that these
men all came from one province, that of which Hong-
Kong is the port, we change, not the induction, but
the area of it ; it concerns not Chinamen but one sort
of Chinamen. So the induction "All crows are black"
was correct for England, but not certainly for the whole
world.

CHAPTER VII.
FACTS OF RESEMBLANCE.

The earliest activities of the infant mind must be in
observing single facts. But there is one recurring fact
of relation which must soon force itself upon the atten-
tion ; this is the resemblance between many of these
single facts. As we say, in popular language, the same
phenomenon is repeated. The word same thus used
means merely that a resembling phenomenon comes.
Meeting a multitude of similar phenomena, the mind at
length forms a general concept, and finally invents a
name which we call a common noun, as mmi or tree.
The existence of such words depends upon the fact of
the existence of numbers of objects recognized by the
mind as similar.

And not only do objects resemble one another, but the
changes and states of objects have also resemblances.
The universe is perceived to be full of lines of resem-
blance or, to use a more common term. Uniformity.
The phenomena about us at this moment are like
the phenomena of yesterday and of a year ago to-day.
" That which hath been is that which shall be ; and that
which hath been done is that which shall be done : and
there is no new thing under the sun. Is there a thing
whereof men say. See, this is nev/.? it hath been already,
in the ages which were before us." ^ As previously
remarked, a universe in which every object should be

1 Ecclesiastes, i. 9, 10.

42 Inductive Logic.

unique and every event a surprising novelty is perfectly
conceivable ; the conception contradicts no law of
thought or, so far as we know, of being. But such is
not the universe in which we live.

As one who enters, for example, a large store of
pottery, soon discovers that much of the stock is in
lots, and that this cup is like other cups, and that
platter like other platters, so the observer of nature
perceives that things are in lots and are passing through
similar changes.

The possibility of language rests upon the recurrence
of resemblances. Not only are objects alike, but their
changes and relations are alike. The words used to
describe the phenomena of yesterday are appropriate
to-day. Nature may be divided into groups of similari-
ties ; and the phrase " Uniformity of Nature " embodies
the opinion that things remain essentially similar to
themselves, and of course, therefore, similar to the
other things which at any time resemble them. Our
belief in the uniformity of nature is the belief that the
quantities and qualities of matter and force, and the
faculties of mind, remain as they are. The integrity of
the existing order is unimpaired.

Long inductive arguments may be constructed by
successive judgments of resemblance, the intuitively
known axiom that things that are equal to the same
thing are equal to each other being the general major
premise. These arguments are therefore mixed induc-
tions. We will add two examples, one from the science
of language and one from the science of geology.

The following analysis of an inductive argument is
taken from Fowler's Inductive Logic. —

Facts of Re setnb lance. 43

" The Method of Concomitant Variations is that which is most
frequently employed in the Science of Language. It is found, for
instance, that between two dissimilar words employed at different
epochs to express the same idea may be interpolated a number of
intermediate forms employed at intermediate epochs, which make
the transition gradual and natural. From this circumstance it is
inferred that the word used at the later epoch is derived from that
used at the earlier epoch, certain tendencies of speech being regarded
as the cause of the divergence. ' Thus, at first sight,' says M.
Brachet, ' it is hard to see that djne is derived from animaj but
history, our guiding-line, shows us that in the thirteenth century
the word was written anine^ in the eleventh aneme^ in the tenth
anime^ which leads us straight to the Latin anijna.'' In this case
there can be no doubt of the truth of the conclusion." ^

This analysis we cannot at all accept. The proof
that ante is the same as anima is based upon a number
of successive observations of facts of resemblance.
Anima and anime are so much alike in look, sound, and
meaning, that we pronounce them the same ; this is
true also of anime and ane7ne, of aneme and anme, of
anme and dme. We therefore construct the equation

anima = dnime = aneme = anme = dme.
.'. ani^na ^=dme.

There is positively nothing here that varies concom-
itantly with the word anima. The explanation that
" certain tendencies of speech are the cause of the
divergence" is just like the explanation that opium
causes sleep because "it has a soporific quality"; it
explains nothing. The method generally employed in
philological investigations is that of direct observation
of resemblances. The proposition that anima and d^ne
are the same word is an induction, because it is the

1 Page 200.

44 Inductive Logic.

statement of a fact not directly observable and the

statement is based upon observations. It is really a

mixed induction ; for it rests upon the axiom that

things that are equal to the same thing are equal to
each other.

Let us try to analyze the following argument for
the evolution of the horse, taken from Le Conte's
Geology : —

" Genesis of the Horse. — In conclusion, it will be interesting
and instructive to run out one of these branches and show in more
detail the genesis of one of the extreme forms. For this purpose
we select the Horse, because it has been somewhat accurately
traced by Huxley and by Marsh. About thirty-five or forty
species of this family, ranging from the earliest Eocene to the
Quaternary, are known in the United States. The steps of evo-
lution may therefore be clearly traced.

"In the lower part of the Eocene basin {Coryphodon beds') of
Green River is found the earliest known animal in the direct line
of descent of the horse family, viz., the recently described
Eohippus of Marsh. This animal had three toes on the hind-foot
and four perfect, serviceable toes on the fore-foot ; but, in addi-
tion, on the fore-foot an imperfect fifth metacarpal (spHnt), and
possibly a corresponding rudimentary fifth toe (the thumb), like a
dew-claw. Also, the two bones of the leg and fore-arm were yet
entirely distinct. This animal was no larger than a fox. Next,
in the Middle Eocene (Bridger beds), came the Orohippiis of
Marsh, an animal of similar size, and having similar structure,
except that the rudimentary thumb or dew-claw is dropped, leav-
ing only four toes on the fore-foot. Next came, in the Lower
Miocene., the Mesohipptis., in which the fourth toe has become a
rudimentary and useless splint. Next came, still in the Miocene.,
the Miohippus of the United States and nearly allied Anchithere
of Europe, more horse-like than the preceding. The rudimentary
fourth spHnt is now almost gone, and the middle hoof has become
larger ; nevertheless, the two side-hoofs are still serviceable. The
two bones of the leg have also become united, though still quite

Facts of Resemblance. 45

distinct. T\As 2si\v[v3\^N2.'s> 2^ovi\. the size of a sheep. Next came,
in the Upper Miocene, and Lower Pliocene, the Protohippus of
the United States and allied Hipparion of Europe, an animal
still more horse-like than the preceding, both in structure and
size. Every remnant of the fourth spHnt is now gone ; the middle
hoof has become still larger, and the two side-hoofs smaller and
shorter, and no longer serviceable, except in marshy ground. It
was about the size of the ass. Next came, in the Plioceiie, the
Pliohippiis, almost a complete horse. The hoofs are reduced to
one, but the splints of the two side-hoofs remain to attest the line
of descent. It differs from the true horse in the skull, shape of
the hoof, the less length of the molars, and some other less im-
portant details. Last comes, in the Quaternary, the modern
horse — Eqtius. The hoof becomes rounder, the splint-bones
shorter, the molars longer, the second bone of the leg more rudi-
mentary, and the evolutionary change is complete.

" Similar gradual changes, becoming more and more horse-like,
may be traced in the shape of the head and neck, and especially
in the gradually increasing length and complexity of structure of
the grinding teeth."

"There can be no doubt that if we could trace the line of
descent still further back we would find a perfect five-toed an-
cestor. From this normal number of five, the toes have been
successively dropped, according to a regular law. In the Perisso-
dactyl line first the thumb. No. i, was dropped; then the little
finger, No. 5 ; then the first and ring-fingers, Nos. 2 and 4, were
shortened up more and more and finally disappeared, and only the
middle finger, No. 3, remained in the modern horse. In the
Artiodactyl line, after the dropping of No. i, then Nos. 2 and 5
of the four-toed foot were shortened and gradually disappeared,
and Nos. 3 and 4 remained in the Ruminants. "

" From the earliest and most generalized types, therefore, to
the present specialized types, the principal changes have been,
first, from plantigrade to digitigrade; second, from short-footed
digitigrade to long-footed digitigrade, i.e., increasing elevation of
the heel; third, from five toes to one toe in the Horse, or two toes
in Ruminants ; and, fourth, from simple omnivorous molars to the
complex herbivorous mill-stones of the Horse and the Ox.

4-6 Inductive Logic.

"The change from plantigrade to digitigrade, with increasing
elevation of the heel, when taken in connection with increasing
size of the brain, and therefore presumably with increasing brain-
power, shows a gradual improvement of structure adapted for
speed and activity, and a pari-passu increase of nervous and
muscular energy necessary to work the improved structure." ^

The foregoing argument is just like that regarding
the words dme and a7iima ; Eohippus so closely resem-
bles OrohippiLS that they must be the same ; Orohippus
must be the same as Mesohippus ; Mesohippus must be
the same as Protohippus; Protohippus is the same as
Pliohippus ; Pliohipptts is the same as E quits ; there-
fore the modern horse is the same as the Eohippus.
The force of this argument will depend upon the
strength of the impressions of resemblance made upon
various minds. Professor Huxley regarded it as
demonstrative.

1 Pages 540-543-

CHAPTER VIII.
FACTS OF COEXISTENCE.

Every observer very quickly perceives that the various
objects in the world may be divided into groups of
permanent coexistences. Here is a mass of matter
with specific gravity 19.34, a yellow color, malleable,
ductile, etc., and there is another mass of matter in
which the same phenomena coexist, and there is an-
other. We call all these masses gold; and we say
that gold is a kind of matter. Malleability, ductility,
etc., are commonly called the properties of gold. But
in truth we know absolutely nothing about gold except
these properties. The weight does not possess the
ductility, nor does the color possess the malleability;
but the coexistence of all these phenomena is gold.

No approach has been made by science to any reason
why certain phenomena permanently coexist ; as, for
instance, why the metal whose specific gravity is 19.34
should be yellow, and the metal whose specific gravity
is 10.5 should be white. It is easy to say that all the
properties probably depend upon some common fact of
causation ; but in the present state of science such a
remark has no meaninsr.

A very large part of the work of science is in ascer-
taining the various natural kinds of objects. Mr. Mill
magnifies the notion of cause and calls it " the root of
the whole theory of induction." But it is plain that the
notion of coexistence is an equally important root.

48 Inductive Logic.

We cannot reason that such and such things must
coexist; we can only discover that they do. This
work has nothing to do with causation. It has nothing
to do with the unknown. It does not proceed by in-
ference. It is the orderly arrangement of what we
know.

One vast attempt of Induction is to classify the
objects in nature, that is, to discover and define all
natural kinds. In this attempt it is soon perceived
that there are groups within groups. Vegetables, for
example, are a natural kind ; but the vegetable king-
dom may be subdivided into more limited kinds, and
these kinds may be again subdivided.

A distinction is made between Natural and Artificial
kinds. We may, for temporary convenience, divide
objects according to some one property, as yellowness.
And then gold and oranges and salmon will be of the
same kind. Such a group is called an Artificial Kind.
But Natural Kinds are so called because the objects
which compose them resemble each other in a multi-
tude of characteristics and appear, in fact, grouped
together by nature. The great botanist Linnaeus
systematized plants according to the numbers of sta-
mens and pistils, neglecting other features. This was
a convenient, but highly artificial, arrangement; since
it brought into the same order plants on the whole
utterly diverse. Modern botany takes into considera-
tion a multitude of particulars in stem, leaf, flower, and
fruit; and so reaches a natural system. No classifica-
tion is natural which depends in the least degree upon
the caprice of the investigator; it must force itself
upon all observers as existing in nature.

Facts of Coexistence. 49

That there is a kind of objects which we may call
plants and another kind of objects which we may call
animals is generally admitted. But when we come to
subdivide the animal and vegetable kingdoms, differ-
ences of opinion arise. It is obvious that certain
individuals greatly resemble one another; they con-
stitute natural groups, which may be called species.
Certain species resemble one another ; they may be
associated in larger groups and called genera. So the
genera may be grouped into orders, and the orders into
classes.

Philosophers have discussed the question whether
there is a point where natural subdivision ends. If
there is such a point, then one of the smallest possible
natural groups would be called an iiifima species. If,
on the other hand, there be a group which cannot
naturally be included in a larger, such a group would
be called a summu7n gemts.

The most interesting question in modern natural
science is, whether the various natural groups of ani-
mals and plants — species, genera, orders, etc. — are
naturally separated by distinct lines. The discussion
has taken the form of an inquiry into the true nature
of species. The main points in it can be conveniently
presented in the words of Professor Asa Gray : —

"The ordinary and generally received view assumes the inde-
pendent, specific creation of each kind of plant and animal in a
primitive stock, which reproduces its like from generation to gen-
eration, and so continues the species. Taking the idea of species
from this perennial succession of essentially similar individuals, the
chain is logically traceable back to a local origin in a single stock,
a single pair, or a single individual, from which all the individuals

50 Inductive Logic.

composing the species have proceeded by natural generation.
Although the similarity of progeny to parent is fundamental in the
conception of species, yet the likeness is by no means absolute ;
all species vary more or less, and some vary remarkably — partly
from the influence of altered circumstances, and partly (and more
really) from unknown constitutional causes which altered condi-
tions favor rather than originate. But these variations are sup-
posed to be mere oscillations from a normal state, and in Nature
to be limited if not transitory ; so that the primordial differences
between species and species at their beginning have not been
effaced, nor largely obscured, by blending through variation.
Consequently, whenever two reputed species are found to blend in
Nature through a series of intermediate forms, community of origin
is inferred, and all the forms, however diverse, are held to belong
to one species. Moreover, since bisexuality is the rule in Nature
(which is practically carried out, in the long run, far more gener-
ally than has been suspected), and the heritable qualities of two
distinct individuals are mingled in the offspring, it is supposed that
the general sterility of hybrid progeny interposes an effectual bar-
rier against the blending of the original species by crossing.

" From this generally accepted view the well-known theory of
Agassiz, and the recent one of Darwin, diverge in exactly opposite
directions.

" That of Agassiz differs fundamentally from the ordinary view
only in this, that it discards the idea of a common descent as the
real bond of union among the individuals of a species, and also
the idea of a local origin — supposing, instead, that each species
originated simultaneously, generally speaking, over the whole
geographical area it now occupies, or has occupied, and in per-
haps as many individuals as it numbered at any subsequent
period.

" Mr. Darwin, on the other hand, holds the orthodox view of
the descent of all the individuals of a species not only from a local
birthplace, but from a single ancestor or pair ; and that each
species has extended and established itself, through natural agen-
cies, wherever it could ; so that the actual geographical distribu-
tion of any species is by no means a primordial arrangement, but
a natural result. He goes farther, and this volume \The Origin

Facts of Coexistence. 51

of S;pecies'\ is a protracted argument intended to prove that the
species we recognize have not been independently created as such,
but have descended, Uke varieties, from other species. Varieties,
on this view, are incipient or possible species ; species are varie-
ties of a larger growth, and a wider and earlier divergence from
the parent stalk ; the difference is one of degree, and not of kind."i

"In applying his principle of natural selection to the work in
hand, Mr. Darwin assumes, as we have seen : (i) Some variability
of animals and plants in nature ; (2) the absence of any definite
distinction between slight variations and varieties of the highest
grade ; (3) the fact that naturalists do not practically agree, and
do not increasingly tend to agree, as to what forms are species and
what are strong varieties, thus rendering it probable that there may
be no essential and original difference, or no possibility of ascer-
taining it, at least in many cases ; also (4) that the most flourish-
ing and dominant species of the larger genera on an average vary
most (a proposition which can be substantiated only by extensive
comparisons, the details of which are not given); and (5) that in
large genera the species are apt to be closely but unequally allied
together, forming little clusters round certain species — just such
clusters as would be formed if we suppose their members once to
have been satellites or varieties of a central or parent species, but
to have attained at length a wider divergence and a specific
character. The fact of such association is undeniable ; and the
use which Mr. Darwin makes of it seems fair and natural.

" The gist of Mr. Darwin's work is to show that such varieties
are gradually diverged into species and genera through natural
selection ; that natural selection is the inevitable resul* oi the
struggle for existence which all living things are engaged in ; and
that this struggle is an unavoidable consequence of several natural
causes, but mainly of the high rate at which all organic beings
tend to increase." ^

" Returning for a moment to De Candolle's article, we are dis-
posed to notice his criticism of Linnaeus's 'definition ' of the term
species {Philosophia Botanica, No. 157): ^Species tot numerainus
quot diversae forrnae in principio S7int creatae'' — which he

^ Darwiniana, p. ii. ^ Ibid., p. 36.

52 Inductive Logic.

declares illogical, inapplicable, and the worst that has been pro-
pounded. ' So, to determine if a form is specific, it is necessary
to go back to its origin, which is impossible. A definition by a
character which can never be verified is no definition at all.'

" Now, as Linnaeus practically applied the idea of species with
a sagacity which has never been surpassed, and rarely equaled,
and, indeed, may be said to have fixed its received meaning in
natural history, it may well be inferred that in the phrase above
cited he did not so much undertake to frame a logical definition,
as to set forth the idea which, in his opinion, lay at the foundation
of species ; on which basis A. L. Jussieu did construct a logical
definition — 'Nunc rectius definitur perennis individuorum similium
successio continuata generatione renascentium.' The fundamental
idea of species, we would still maintain, is that of a chain of which
genetically connected individuals are the links. That, in the prac-
tical recognition of species, the essential characteristic has to be
inferred, is no great objection — the general fact that like engen-
ders like being an induction from a vast number of instances, and
the only assumption being that of the uniformity of Nature. The
idea of gravitation, that of the atomic constitution of matter, and
the like, equally have to be verified inferentially. If we still hold-
to the idea of Linnaeus, and of Agassiz, that existing species were
created independently and essentially all at once at the beginning
of the present era, we could not better the propositions of Linnaeus
and of Jussieu. If, on the other hand, the time has come in which
we may accept, with De Candolle, their successive origination, at
the commencement of the present era or before, and even by
derivation from other forms, then the ' /;/ principio ' of Linnaeus
will refer to that time, whenever it was, and his proposition be as
sound and wise as ever." ^

"... Species, as I have said (in Sillintan''s Journal articles)
are not facts or things, but judgments, and, of course, fallible
judgments. How fallible, the working naturalist knows and feels
more than any one else." ^

Inductive Classificatio7i is the orderly arrangement of
things in their natural groups or kinds. We may

1 Darwiniana, p. 201. ^ Letters., p. 657.

Facts of Coexistence. 53

classify mental states or social movements, as well as
physical forces and material objects, minerals, plants,
and animals.

Nomenclature is a system of names for the various
things classified. In Botany the name of a plant is
always in Latin, and consists of the name of the genus,
followed by the name of the species, as Viola blanda,
sweet white violet. Unfortunately, no one has yet
thought of any way of forming botanical names from
natural characteristics, so that the nomenclature, also,
may be natural. On the contrary, the names of genera
and species have been assigned by discoverers for trivial
and often ridiculous reasons, and the whole scientific
world has been forced to perpetuate the memory of silly
caprices. This is an ignominy which no disciplined
mind can think of without indignation. In Chemistry
the names of substances are compounded of those of
their elements, with prefixes and terminations suggest-
ing their proportions. Chemical nomenclature is the
best we have, but its development has lagged behind
the general progress of the science. Mineralogy needs
nothing more than an adequate nomenclature. A
system of names suggesting both crystallography and
chemical composition would be far preferable to smith-
ite, jonesite, and brownite.

Terminology is the precise vocabulary used in describ-
ing the parts, qualities, and actions of the objects of
science. Botany has a wonderfully copious vocabulary.
This vocabulary is strictly inductive ; the meaning of
each word is fixed by direct examination of typical
specimens. Such words as serrate, dentate, crenate,
runcinate, bipinnatifid, etc., are defined by exhibiting

54 Inductive Logic.

to the learner the parts of plants which they describe,
and each is ever afterwards used in precisely the same
sense. By the use of a proper terminology, scientists
can convey to one another, in a few words, accurate
descriptions of phenomena, which pages of popular
phraseology would leave still obscure.

CHAPTER IX.

FACTS OF CAUSATION AND FACTS OF
SUCCESSION.

It is a matter of observation that things in this
universe react upon one another. It is further observed
that after such reactions the things sometimes appear
in new forms. This property of reacting, or of present-
ing new forms, is called the power of Causation. The
several reactions of things are called events. The
things which react are said to be the causes of these
events. If things appear in new forms, they are said
to be, in their antecedent forms, the causes of them-
selves in their subsequent forms.

This power of affecting, or being affected, is an
ultimate property of things. It is one of those ulti-
mate properties the coexistence of which constitutes
the existing order. Science never attempts the explana-
tion of ultimate properties ; or rather, when science
finds anything inexplicable she calls it ultimate.

Things exist in space, and events occur in time.
Time is marked and estimated by the succession of
events. And these events are seen to have often a
certain relation to one another. Just as there are cer-
tain uniform coexistences of phenomena, so there are
certain uniform successions. Yellowness and ductility
present themselves simultaneously in gold ; contact
with red-hot iron and pain in the flesh present them-

56 Inductive Logic.

selves as antecedent and consequent events. The
events of history seem to come in chains, one link
drawing on the next. So impressed have some philoso-
phers been with this appearance of concatenation among
events, that they have attempted to define causation
itself in terms of succession, and they have thus brought
great confusion into the science of inductive logic.

Perhaps it may be easier to define the difficult word
Cause, and to show the relation of causation and suc-
cession, in connection with a concrete example. We
will, therefore, take an instance classic in the history
of inductive science, one of the experiments of the
illustrious Count Rumford upon heat. The illustration
will be useful not only here but in subsequent chapters,
and it is so interesting that we will give it at length,
and in the Count's own words.

" Being engaged lately in superintending the boring of cannon
in the workshops of the miUtary arsenal at Munich, I was struck
with the very considerable degree of heat which a brass gun
acquires, in a short time, in being bored ; and with the still more
intense heat, much greater than that of boiling water, as I found
by experiment, of the metallic chips separated from it by the
borer. From whence comes the heat actually produced in the
mechanical operation above-mentioned? . . .

"... Taking a cannon, a brass six-povi,ider, cast solid, and
rough as it came from the foundry, and fixing it horizontally in
the machine used for boring, and at the same time finishing the
outside of the cannon by turning, I caused its extremity to be cut
off ; and, by turning down the metal in that part, a solid cylinder
was formed, 7|- inches in diameter, and c)-^^ inches long ; which,
when finished, remained joined to the rest of the metal, that which,
properly speaking, constituted the cannon, by a small cylindrical
neck, only i\ inches in diameter, and 3^^^ inches long. This
short cylinder, which was supported in its horizontal position, and

Facts of Catisation and Facts of Succession. 57

turned round its axis, by means of the neck by which it remained
united to the cannon, was now bored with the horizontal borer
used in boring cannon ; but its bore, which was 3.7 inches in
diameter, instead of being continued through its whole length, 9.8
inches, was only 7.2 inches in length ; so that a solid bottom
was left to this hollow cylinder, which bottom was 2.6 inches in
thickness.

" The cyhnder being designed for the express purpose of gener-
ating heat by friction, by having a blunt borer forced against its
solid bottom at the same time that it should be turned round its
axis by the force of horses, in order that the heat accumulated in
the cylinder might from time to time be measured, a small round
hole, 0.37 of an inch only in diameter, and 4.2 inches in depth, for
the purpose of introducing a small cylindrical mercurial thermom-
eter, was made in it, on one side, in a direction perpendicular to
the axis of the cylinder, and ending in the middle of the solid
part of the metal which formed the bottom of its bore.

^^ Exper. J. — A quadrangular oblong deal box, water-tight,
iii English inches long, 9^^ inches wide, and 9^^^ inches deep,
being provided, with holes or slits in the middle of each of its
ends, just large enough to receive, the one, the square iron rod to
the end of which the blunt steel borer was fastened, the other, the
small cylindrical neck which joined the hollow cylinder to the
cannon ; when this box was put into its place it was fixed to the
machinery, in such a manner that its bottom being in the plane of
the horizon, its axis coincided with the axis of the hollow metallic
cylinder ; it is evident, from the description, that the hollow
metallic cylinder would occupy the middle of the box, without
touching it on either side ; and that, on pouring water into the
box, and filling it to the brim, the cyhnder would be completely
covered, and surrounded on every side, by that fluid. And further,
as the box was held fast by the strong square iron rod which
passed, in a square hole, in the centre of one of its ends, while the
round or cylindrical neck, which joined the hollow cylinder to the
end of the cannon, could turn round freely on its axis in the round
hole in the centre of the other end of it, it is evident that the
machinery could be put in motion, without the least danger of
forcing the box out of its place, throwing the water out of it, or

58 Inductive Logic.

deranging any part of the apparatus. Everything being ready, I
proceeded to make the experiment I had projected, in the follow-
ing manner.

" The hollow cylinder having been previously cleaned out, and
the inside of its bore wiped with a clean towel till it was quite dry,
the square iron bar, with the blunt steel borer fixed to the end of
it, was put into its place ; the mouth of the bore of the cylinder
being closed at the same time, by means of the circular piston,
through the centre of which the iron bar passed. The box was
then put in its place, and the joinings of the iron rod, and of the
neck of the cylinder, with the two ends of the box, having been
made water-tight by means of collars of oiled leather, the box was
filled with cold water (viz., at the temperature of (id^^, and the
machine was put in motion. The result of this beautiful experi-
ment was very striking, and the pleasure it afforded me amply
repaid me for all the trouble I had had, in contriving and arrang-
ing the complicated machinery used in making it. The cylinder,
revolving at the rate of about 32 times in a minute, had been in
motion but a short time, when I perceived, by putting my hand
into the water, touching the outside of the cylinder, that heat was
generated ; and it was not long before the water which surrounded
the cylinder began to be sensibly warm. At the end of i hour,

1 found, by plunging a thermometer into the water in the box (the
quantity of which fluid amounted to 18.77 lb. avoirdupois, or 2.\
wine gallons), that its temperature had been raised no less than
47 degrees, being now 107° of Fahrenheit's scale. When 30
minutes more had elapsed, or i hour and 30 minutes after the
machinery had been put in motion, the heat of the water in the
box was 142°. At the end of 2 hours, reckoning from the begin-
ning of the experiment, the temperature of the water was found to
be raised to 178°. At 2 hours 20 minutes it was at 200°; and at

2 hours 30 minutes it actually boiled.

" It would be difficult to describe the surprise and astonishment
expressed in the countenances of the by-standers, on seeing so
large a quantity of cold water heated, and actually made to boil,
without any fire. Though there was, in fact, nothing that could
justly be considered as surprising in this event, yet I acknowledge
fairly that it afforded me a degree of childish pleasure, which,

Facts of Causation and Facts of Sziccession. 59

were I ambitious of the reputation of a grave philosopher, I ought
most certainly rather to hide than to discover." ^

Here is a phenomenon — the heat of the water in
Count Rumford's box. Let us inquire now what we
are doing when we seek for its cause.

Plainly the motion of the cylinder was an antecedent
of the heat in the water in some pre-eminent and unique
sense. Heat is an energy ; it could not appear in the
wafer unless it passed out of some other material in
which it previously existed as motion, or in some other
mode. We know this by a very broad primary induc-
tion. Indeed, we here come upon the grand generaliza-
tion of the conservation, or, to use a better word, the
persistence, of energy. A multitude of experiences
have led men to believe that whenever energy newly
appears, it has existed previously in another mode or in
other materials. The necessary antecedent of energy
in one mode or one body is the same energy in a pre-
vious mode or in a different body. All machinery is
contrived on this principle ; at some point energy is
introduced, and it is then transferred or transformed,
so that we get light, heat, electricity or motion, as
desired. From the standpoint of the physicist the
whole cause of the heat of the water was the motion
of the cylinder. The degree of heat gained by the one
was exactly measured by the amount of motion lost by
.the other. There was only a transfer of energy. When
in popular language we say that the motion is the
cause of the heat, the physicist says that the motion is
the heat, only in another mode. The law of causation,
when applied to energy, is only the fact of persistence.

1 Fktl. Trans. Royal Soc. of London, vol. xviii, pp. 278-282.

6o Inductive Logic.

When we say that energy here must have had a cause,
we only mean that, having no reason to think that new
energy has been added to the world, we must conse-
quently assume that this apparently new energy is only
the old in a new mode. When, therefore, we inquire
for the cause of energy, we may be merely inquiring,
Where and in what mode was this energy previously ?
The answer to the question names the Energetic Cause.
If it be asked. What was the cause of the motion in
the cylinder ? the answer is. The motion of the horses.
The energy might be further traced through physio-
logical action in the bodies of the horses, and then
through physiological action in the growth of the grain
and hay upon which they had fed, until at last we
should reach the sun's light and heat. One thing is
now agreed upon, that the stream of energy in the
world, like the Nile in the desert, receives no tributaries,
but simply flows on identical with itself, its transforma-
tions depending upon the qualities and collocations of
matter.

But why did motion in the cylinder become heat in
the water .<* Here a cause is demanded in a different
sense. The inquiry is for those properties and colloca-
tions of matter which occasioned a transformation. The
arrangement was such that motion could not be com-
municated from the cylinder to any other part of the
apparatus ; the motion, therefore, according to a per-
manently coexisting property, transformed itself into
heat. The different properties of energy and the dif-
ferent properties of the several sorts of matter in rela-
tion to energy, we know by primary inductions which
cannot be resolved into simpler generalizations ; they

Facts of Causation and Facts of Siiccession. 6 1

are the ultimate facts of the world. The motion of the
cylinder changed into heat when the cylinder found
itself in connection with certain other masses of matter
of certain qualities and collocations. What were these ?
The answer to this question will name the Conditional
Canse. It will describe the environment in which the
transformation took place. While the motion was the
cause, and in one sense the sole cause, of the heat, it
is yet true that, if left to itself, it would never have
changed to heat ; it would have continued eternally as
motion. The peculiar environment, then, is, in one
sense, the sole cause of the heat, since but for that
there would have been nothing but motion.

If, instead of investigating the cause of the energy in
this experiment, we should investigate the cause of the
matter, asking not. What is the cause of the heat t but,
What is the cause of the water ? we could go back in
the same way along an unbroken line of materials. The
cause of the water in the box was water in a river or a
well, the cause of that was water in the clouds, the
cause of that was the two gases oxygen and hydrogen,
and so on. There is a persistence of matter as there
is a persistence of force. When we ask for the cause
of matter in one form or place we may be merely
inquiring, Where and in what form was this matter
previously .? The answer will name for us the Material
Canse. Or we may seek the conditional cause for the
matter, asking. What was the environment in which this
matter came to be as it is ">.

According to one of the grandest primary induc-
tions of modern science, the two lines of energetic and
material causation are absolutely continuous and com-

62 Inductive Logic.

plete. In the physical world nothing is added and
nothing is lost ; but the sum of things persists in its
integrity.

But approaching the analysis upon a different line,
we find that Count Rumford himself was in a unique
sense the cause of the heat. It was his, choice to per-
form an experiment that eventuated in the heating.
The Will of Count Rumford was neither the material
cause, nor the energetic cause, nor the conditional cause
of the heating of the water. It was the cause in a
sense higher than any of these. We will call it the
Volitional Cause. The relation of will to the physical
universe is peculiar. It cannot originate matter or
energy; but it can direct the transformation of a
certain amount of the energy of the body. By taking
advantage of this power, the Count originated a new
chain of events, which terminated in the heating.
When in pursuing a chain of events backward we
come to a will, the mind recognizes a super-physical
intervention ; the man is responsible, and if the events
are injurious to the public welfare, he must pay the
penalty. All of the power now in my arm was yester-
day, or previously, in the beef, potatoes, and other food
on the table. If I allow my arm to hang limp, physi-
ological and chemical transformations will go forward
in natural course, and the energy now potentially mine
will pass away. For a brief space this stored energy
lies subject to my order, like money in a bank. I can
will its transformation into motion ; but I cannot
increase or diminish its amount. A party of Arctic
explorers, after many days of starvation and hard labor,
attempted to draw their boat out of the water ; all

Facts of Causation and Facts of Succession. 63

grasped it and at the accustomed signal put forth the
usual volition for simultaneous action. But no effect
followed ; their wills were as usual, but there was no
stored energy for those wills to transform.
Lotze has said : —

"What constitutes the absolute authority of the causal law is not
that every part of the finite sum of things actual must in the finite
sphere be produced by fixed causes, according to universal laws,
but that each constituent once introduced into this actual course
continues to act according to these laws. We commonly speak
only of every effect having its cause, but we should on the con-
trary lay stress chiefly on the other form of the proposition —
every cause has invariably its effect. The meaning of causahty
consists not indeed exclusively, but (it seems to me) in its more
essential part, in its securing to every element of the actual world,
springing from no matter what source, means of acting energetic-
ally on the other constituents of the world to which it belongs, at
the same time preventing it from acting within that world otherwise
than in harmony with the universal laws regulating all that takes
place in it. Thus the world would be like a vortex swelled by
new waves from all sides, which it does not itself attract or
produce, but which, once within it, are forced to take part in its
motion. We have another example of the same process in the
relation of our own soul to our bodily organs ; the soul evolves
from itself resolutions, starting-points for future movements ; none
of them needs to be determined by and founded on phenomena
in the bodily life on which it reacts ; but each, at the moment of
its passing into that life, subordinates itself to the peculiar laws of
the latter, and generates so much or so little motion and force as
these permit of — motion too in the direction which they prescribe
and no other. The universal course of things may at every
moment have innumerable beginnings whose origin lies outside of
it, but can have none not necessarily continued within it." ^

1 Microcosmus, p. 260. I am indebted for this quotation to my col-
league, Professor Henry C. King.

64 Inductive Logic.

Lotze is wrong in saying that the will generates
force and thus adds to the sum of physical things ; but
he is right in saying that the spiritual acts upon the
physical to transform energy, and that, once transformed,
the energy goes on acting according to the uniformity
of its coexistences, or what are commonly called its
laws. The beginnings which lie outside of the uni-
versal course of physical things are volitions, and their
effects are transformations. The will is not the ener-
getic cause any more than it is the material cause ; it
is a cause stu generis, the volitional cause.

So far we have spoken of Things as the causes of
Things. Matter in one form or situation is the cause
of the same matter differently disposed ; energy as
motion is the cause of the same energy as heat ; a
Will, by transforming the vital energy of the body into
various motions, brings together matter and energy in
new combinations. The causes so far considered are
entities and the effects are entities.

But things may also cause Events. Every kind of
matter and every kind of energy has uniform properties ;
it reacts in certain ways upon other things. These
reactions are called its effects. In this aspect each
thing may be called an Efficient Cause. In our exper-
iment there were certain events, the moving of the
cylinder, the heating of the water, etc. The energy
concerned was the efficient cause of these events.
Count Rumford was also an efficient cause of the
events, since the action of his will was concerned in
their production.

But an entirely different line of investigation might
have been pursued ; leaving things entirely out of view,

Facts of Causation and Facts of Succession. 65

we might have attended solely to Events. One event
may be said to cause another event.

The ultimate qualities of matter and force remaining
as they are, in every possible collocation of things
(except that of perfect equilibrium), a certain reaction
is inevitable. If, for example, it be the nature of water
to absorb heat, then when a quantity of water, as in
Count Rumford's box, finds itself in contact with a hot
cylinder, the absorption will inevitably take place. But
every physical event is simply a new distribution of
forces and materials : hence (the properties of things
remaining as they are) a further reaction is inevitable.
Thus, like the bits of colored glass in a kaleidoscope,
the things in the physical world fall at each moment
into new relations each of which, if there be no inter-
vention, is the necessary opportunity for the next.
Thus one event is said to cause another event. This
inevitableness of physical reaction is the very fact
which opens the door for the interventions of will.
By transforming the energy of the body into motion,
and thus changing the collocations of a few things,
men shunt on to other tracks the trains of events and
transform the whole complexion of history.

Recurring to the experiment, we may say that the
moving of the cyhnder was an event which caused the
heating of the water, another event. But when rigid
definition is attempted it is found surprisingly difficult
to define an event. The event was not merely the
heating of some water, but the heating of it in a cer-
tain box at a particular time and place and in peculiar
circumstances. When all the circumstances, even the
most remote, are taken into the account, they include

66 Inductive Logic.

the situation of the whole universe. The successive
events of history are the successive collocations of the
totality of things. While this is true, the general facts
of the universe are so permanent and so similar as
factors in all events that they may be practically dis-
regarded, and the more detailed and proximate elements
alone considered as constituting an event. The name
Historical Cause may be given to one event when
regarded as the cause of another event. Notice how
different is the sense of the word cause here from that
which it bears when applied to things. An event is
the cause of another event only in the sense that its
occurrence is the coming of materials and forces into
such a collocation that they are certain to react again
in a particular way. The turning of the cylinder was
an event ; but if a cylinder be turning under such
circumstances, it is the ultimate property of motion to
become heat and of water to absorb heat; consequently
the turning was the historical cause of the heating.
Between events there can be no connection but that of
succession ; they are but the coming of things into
collocations. The continuity is in the things, and each
new event arises out of the ultimate properties which
coexist in things. There is no efficiency in an event,
or tendency of any kind to beget another event; but
after each event there is a new possibility; and, the
properties of matter and force remaining persistent,
whatever is possible is inevitable. When a siphon has
been filled with water and is left open, the force of
gravity will cause the water to flow until the short end
of the tube is exposed. The filling and opening of the
siphon are events which leave a situation in which

Facts of Causation and Facts of Succession. 6/

gravity can cause a flow, but those events have no
efficiency in inducing the flow. Popularly, the fall-
ing of a spark into a powder magazine is said to cause
an explosion. Historically this is correct ; when a
spark so falls there is a collocation in which heat will
pass into materials which at that temperature will enter
into new chemical combinations accompanied by that
sudden distension which is called an explosion. The
falling of the spark is the historical cause, the spark
and the powder are the material cause, the heat of the
spark and the chemical affinity of the substances con-
stituting the powder are the energetic cause.

In a loose way, an event may be said to be the cause
of a State. A blackened pile of ruins may be pointed
out as the effects of a conflagration, or the splintered
trunk of a tree may be called the effect of lightning.
But, strictly speaking, states have no causes. No
reason need be given why things remain as they are ;
for obviously, unless something happens, nothing hap-
pens. If a ball is in motion, and no obstruction
presents itself, we do not have to account for the
motion ; but if the ball stops, there is an event to
account for. An event is the coming of things into a
new situation. If in this situation there is a com-
parative equilibrium of forces, the situation may
indefinitely continue. If the breaking of a dam allows
the water to flow out, the event of the breaking is the
historical cause of the event of the emptying. But the
reservoir may never be filled again ; the state of empti-
ness may continue permanently, and the cause for it
will be said to be the breaking of the dam. This,
however, is a very inexact use of language. Emptiness

6S Inductive Logic.

is a mere negation. The thing to be accounted for is
the change from the previous fullness. The breach in
the dam leaves the water free to move, under the
efficient cause, gravity ; once empty, the reservoir
remains so without needing a cause of any kind.

Human history moves on in the midst of a complex
of materials and forces which have certain properties,
and which are certain, in each given collocation, to react
in one particular way. Physically speaking, whatever
at any moment is possible is certain. There is no
contingency, no alternative. A weight free to fall
falls; a bit of iron in a jar of oxygen and sufficiently
hot burns. Each event makes possible the next, and
in that sense may be said to make it certain. But the
human will has the wonderful power of choosing which
of several events shall come to pass. It cannot create
nor annihilate matter or energy ; but it can transform
the energy of the body into motion. Thus materials
and forces may be brought into collocations which
would not otherwise have arisen and, although reacting
according to their nature, may produce events very
different from what would otherwise have been. The
volitions of will do not arise by necessity out of fore-
going situations; consciousness affirms freedom, and it
is here our only organ of observation. The motives
in view of which will acts are Occasional Causes, not
efficient causes. In tracing the course of events in
human history we find this interweaving of physical
necessities and free volitions like the warp and woof of
a tapestry : to unravel it, is the task of the historian in
his search for the connections of things. A passage
from the Life and Letters of Charles Darwin will show

Facts of Causation and Facts of Succession. 69

how slight may be the connection between two events
which are yet in a certain sense cause and effect : —

"The following story shows what good guesses my father
could make. Lord Shelburne, afterward the first Marquis of
Lansdowne, was famous (as Macaulay somewliere remarks) for his
knowledge of the affairs of Europe, on which he greatly prided
himself. He consulted my father medically, and afterward
harangued him on the state of Holland. My father had studied
medicine at Leyden, and one day while there went on a long walk
into the country with a friend who took him to the house of a

clergyman (we will say the Rev. Mr. A , for I have forgotten

his name), who had married an Englishwoman. My father was
very hungry, and there was little for luncheon except cheese,
which he could never eat. The old lady was surprised and
grieved at this, and assured my father that it was an excellent
cheese, and had been sent to her from Bowood, the seat of Lord
Shelburne. My father wondered why a cheese should be sent to
her from Bowood, but thought nothing more about it until it
flashed across his mind many years afterwards, whilst Lord
Shelburne was talking about Holland. So he answered, 'I should

think from what I saw of the Rev. Mr. A , that he was a very

able man, and well acquainted with the state of Holland.' My
father saw that the Earl, who unmediately changed the conver-
sation, was much startled. On the next morning my father
received a note from the Earl, saying that he had delayed starting
on his journey, and wished particularly to see my father. When
he called, the Earl said, 'Dr. Darwin, it is of the utmost impor-
tance to me and to the Rev. Mr. A to learn how you have

discovered that he is the source of my information about Holland.'
So my father had to explain the state of the case, and he supposed
that Lord Shelburne was much struck with his diplomatic skill in
guessing, for during many years afterwards he received many kind
messages from him through various friends. I think that he
must have told the story to his children ; for Sir C. Lyell asked
me many years ago why the Marquis of Lansdowne (the son or
grandson of the first marquis) felt so much interest about me,
whom he had never seen, and my family. When forty new mem-

70 Inductive Logic.

bers (the forty thieves, as they were then called) were added to
the Athenaeum Club, there was much canvassing to be one of
them ; and without my having asked any one. Lord Lansdowne
proposed me and got me elected. If I am right in my supposi-
tion, it was a queer concatenation of events that my father not
eating cheese half-a-century before in Holland led to my election
as a member of the Athenaeum." ^

This " queer concatenation " is a fair example of
causation in human history. Dr. Darwin's not eating
cheese was the cause of his son's being elected into
the club, that is, it was a link in a chain of events,
some of which were volitions and some physical neces-
sities, and the election was a subsequent link. The
very triviality of this incident makes it especially good
as an illustration. We have termed the motives upon
which the will reacts, occasional causes, since they
furnish the occasions, but not the efificiency, of causa-
tion. Here maybe distinguished the Formal Cause, or
idea viewed as a distinct conception ; and Final Cause,
the end, design, or object for which anything is done.

A Negative Cause is the absence of anything which if
present would have prevented a given phenomenon. It
is obvious that any particular event would not have
happened if it had been prevented. The absence of a
violent earthquake was a negative cause of the heating
of the water in Count Rumford's experiment. But the
word cause is used here in a sense very remote from
that which it bears in other connections. A little boy
said that salt was the cause of a bad taste in potatoes
when he did not put it on them. That is, in the
absence of salt, potatoes have an insipid taste. To say
"negative cause" is, indeed, to make a contradiction

1 Page 14.

Facts of Causation and Facts of Succession. 71

in the adjective ; it is equivalent to "inactive agent."
But in common life, and in ordinary discourse, it is
convenient, when the absence of some usual factor in
a collocation of things gives opportunity for some
unusual event. Thus the absence of the signalman is
said to be the negative cause of the railway accident,
and the sleep of the sentinel is said to be the negative
cause of the defeat of the army. A will may be a
negative cause in a more active sense, since refusal to
interfere, when interference is possible, involves at least
consent to the occurrence of the event; hence, neglect
may be criminal.

Let us sum up now the results of our discussion of
Causation. The cause of a phenomenon is that which
gives it existence. Every mass of matter has a mate-
rial cause, which is the same matter in a previous place
or state. Every portion of energy has an energetic
cause, which is the same energy in a previous mode or
another mass of matter. Every portion of matter or
of energy has a conditional cause for its present place
and form, in the environment which has reacted upon it.
One peculiar factor in the conditional cause may be a
will whose reaction transforms energy, thus constitut-
ing a volitional cause. A will acts in view of motives,
occasional causes. Events are the reactions of things,
which are their efficient causes.

Is the law of causation, namely, that every phenome-
non depends upon some other phenomenon, intuitively
known } The question is too vague to admit of a
single answer. That matter and energy persist is a
very recently made primary induction from experience.
The law of material and of energetic causation is, then.

72 Inductive Logic.

not intuitively known. That every event has a thing
as its cause is known by a mere analysis of the mean-
ing of the terms employed, since events are the reactions
of things, and there cannot be an action without an
agent. That every event has some other event as its
necessary historical cause is not proved either from
intuition or experience. Gravitation causes the earth
to revolve around the sun ; the causation is in the
bodies and forces, not in any previous event. That a
will acts in view of final and formal causes is plain ;
but that, like matter, it always reacts in precisely the
same way under the same stimulus is contradicted by
consciousness.

Do we know intuitively that "like causes always
produce like effects " t The difficulty with this ques-
tion is that the words cause and effect are correlatives,
and must be defined in terms of each other. An
affirmative answer would teach nothing but an identical
proposition. The truth which the dictum seeks to
express is better stated thus : We know by a primary
induction that the existing order persists, and while
things remain as they are they will act as they do.
How long the existing order will continue we cannot
even guess, since all of our reasoning about things is
based upon primary inductions from the existing order.
But neither have we any ground for expecting an end.

The foregoing discussion of facts of causation makes
it easy to deal with facts of succession. The facts of
succession are seen to be all secondary. They are
incidental results of facts of causation. Succession is
not at all of the essence of causation. Gravitation
keeps the earth revolving around the sun. This effect

Facts of CaiLsation and Facts of Succession. 73

is the operation of a permanent cause — the two bodies
reacting upon each other ; but there is no succession
of cause and effect. Just so the needle is attracted
toward the pole by a permanent cause, magnetism.
Succession belongs to events in their mutual relations,
not to things ; but things are the only efficient causes.
Things coexist and persist ; they do not follow one
another in time. It is true that between a thing and
the material cause of it, that is, the same matter in an
earlier form, there is a sort of succession. Ice may
cause water, and water may cause steam ; one form
follows another. But this is not at all that invariable
sequence which constitutes a fact of succession. Things
must be simultaneous with their own reactions. Pro-
fessor Davis remarks: —

" But it would, perhaps, be more accurate to say that every cause
is simultaneous with its effect. For cause and effect are correla-
tives— neither can exist without the other; they exist only as
they coexist. A cause cannot be so named, except by anticipation,
until there is an effect ; nor an effect, except by reference to what
has already occurred, after the change or event has taken place.
The order of succession is logical, not temporal." ^

The fact that events occupy time, and the fact that
each event leaves a new collocation of things which
makes a new reaction possible — these two facts give
us the chain of history. Between two events, one of
which is the historical cause and the other the his-
torical effect, there is no other connection than that,
after the first, things are in such a collocation that they
cause the second. An event has as many possible
historical causes as there are possible ways of bringing

1 Inductive Logic, p- 23.

74 Inductive Logic,

things into the requisite collocation. For example, ice
when in contact with salt at ordinary temperatures of
the air rapidly liquefies. The efficient cause of the
event, liquefaction, is the two bodies ice and salt, and
they are simultaneous with it. But the historical cause
of the event is any possible action which can bring the
substances together, and thus open the possibility for
their reaction. All facts of succession are thus conse-
quences of facts of coexistence and causation. A
succession is known empirically, and is susceptible of
analysis into simpler elements. We may always hope
to be able to tell why a given succession obtains, in
terms of facts of coexistence and causation. Yet many
successions were empirically known ages before they
were analyzed, and many well-known successions still
remain unanalyzed. Many persons are familiar with
that historical succession of events which always ends
in the production of ice-cream, who have never thought
of the operation of the efficient causes.

CHAPTER X.
MR. MILL'S DOCTRINE OF CAUSATION.

Mr. John Stuart Mill is unquestionably the most
eminent and influential of all writers upon inductive
logic since Bacon. His work is the most elaborate
that has appeared, and his teachings, on many points,
have been generally adopted. The science owes to him
a very great debt. No one can justly claim to under-
stand modern inductive logic who has not thoroughly
studied Mr. Mill's doctrine of causation. In this
chapter we shall seek to present this doctrine in a
condensed form, but as nearly as possible in Mr. Mill's
own words.

According to Mr. Mill, the notion of cause is "the
root of the whole theory of Induction." In this view
he is followed by later writers. For example. Professor
Davis says : " Such principles are evolved from the
intuitive fact of causation, the root of all induction,
and that which gives it validity."

Yet Mr. Mill also holds that our first step in the
knowledge of nature is to discover the particular
uniformities; then that we generalize the uniformity
of these uniformities ; and that this uniformity of
uniformities is the law of the uniformity of nature.
Strangely enough, the uniformity of nature is, to Mr.
Mill, the same as the law of causation. " Whatever be
the most proper mode of expressing it," he says, "the
proposition that the course of nature is uniform, is the
fundamental principle, or general axiom of induction."

"J 6 Inductive Logic.

It is a difficulty with this view that if inductive logic
have to do solely with causation, the vast mass of facts
of coexistence and of resemblance is left unprovided
for. Such sciences as mineralogy and botany deal
mainly with facts of coexistence, yet they are com-
monly considered purely inductive. The definition
provides no rightful place in inductive logic for the
original discovery of uniformities; all of this work has
been done before induction proper can begin. More-
over, the law of uniformity of uniformities is something
very much wider than the law of causation. It is
largely concerned with the uniformities of coexistence.
Thus we know the persistence of the several kinds of
matter and the persistence of energy by so many inde-
pendent primary inductions from multitudinous obser-
vations of the several things. We not only know that
a magnet attracts iron, which is a fact of causation;
but that iron remains iron, that is, that that assemblage
of coexisting qualities which we call iron persists,
which is not a fact of causation.

Mr. Mill does not regard the uniformity of nature as
"the immediate major premise in every inductive argu-
ment." " It is not a necessary condition that the
uniformity should pervade all nature. It is enough
that it pervades the particular class of phenomena to
which the induction relates." That is, we may make a
valid secondary induction from any sound, though
limited, primary induction, without reference to the
soundness of the root of the whole theory. In fact the
so-called root is only a generalization of more limited
primary inductions.

Mr. Mill's definition of Cause is as follows : —

Mr. Mill's Doctrine of Causation. J'J

" We may define, therefore, the cause of a phenomenon, to be
the antecedent, or the concurrence of antecedents, on which it is
invariably and unconditionally consequent."

In making this definition Mr. Mill began with no
analysis of the different ways in which the word cause
is used. He did not inquire whether the so-called
effect is a thing or a reaction, or the so-called cause a
material, an energy, a circumstance, a will, or a prior
event. Starting with the notion of succession as
fundamental, he attempted to frame a definition so
general as to cover all values of the unknown terms of
the relation. Yet it is plain in the course of his
elaborate discussions that, generally, for him the
"phenomenon" in the definition is a reaction, an
event. For he says : —

"And the universality of the law of causation consists in this,
that every consequent is connected in this manner with some par-
ticular antecedent, or set of antecedents. Let the fact be what it
may, if it has begun to exist, it was preceded by some fact or
facts, with which it is invariably connected. For every event
there exists some combination of objects or events, some given
concurrence of circumstances, positive and negative, the occur-
rence of which is always followed by that phenomenon." "On
the universality of this truth depends the possibility of reducing
the inductive process to rules." ^

For Mr. Mill, then, an effect is an event, and a cause
is a number of things in a collocation and with a
history.

In this complex of things, relations, and history, to
which alone Mr. Mill, when speaking strictly, gives the
name cause, all the factors are absolutely equal. The

1 Logic, p. 237.

y8 Inductive Logic.

difference between efficient causes and conditions is
denied. Mr. Mill says : —

"It is seldom, if ever, between a consequent and one single
antecedent, that this invariable sequence subsists. It is usually
between a consequent and the sum of several antecedents; the
concurrence of them all being requisite to produce, that is, to be
certain of being followed by, the consequent. In such cases it is
very common to single out one only of the antecedents under the
denomination of Cause, caUing the others merely Conditions.
Thus, if a man eats of a particular dish, and dies in consequence,
that is, would not have died if he had not eaten of it, people would
be apt to say that eating of that dish was the cause of his death.
There need not, however, be any invariable connection between
eating of the dish and death; but there certainly is, among the
circumstances which took place, some combination or other upon
which death is invariably consequent : as, for instance, the act of
eating of the dish, combined with a particular bodily constitution,
a particular state of present health, and perhaps even a certain
state of the atmosphere; the whole of which circumstances, per-
haps, constituted in this particular case the conditions of the
phenomenon, or in other words, the set of antecedents which
determined it, and but for which it would not have happened.
The real Cause, is the whole of these antecedents; and we have,
philosophically speaking, no right to give the name of cause to
one of them, exclusively of the others. What, in the case we have
supposed, disguises the incorrectness of the expression, is this:
that the various conditions, except the single one of eating the
food, were not events (that is, instantaneous changes, or succes-
sions of instantaneous changes) but states, possessing more or less
of permanency; and might, therefore, have preceded the effect by
an indefinite length of duration, for want of the event which was
requisite to complete the required concurrence of conditions: while
as soon as that event, eating the food, occurs, no other cause is
waited for, but the effect begins immediately to take place: and
hence the appearance is presented of a more immediate and closer
connection between the effect and that one antecedent, than
between the effect and the remaining conditions. But though we

Mr. Mill's Doctrine of Causation. 79

may think proper to give the name of cause to that one condition
the fulfillment of which completes the tale and brings about the
effect without further delay, this condition has really no closer
relation to the effect than any of the other conditions has. All the
conditions were equally indispensable to the production of the
consequent; and the statement of the cause is incomplete, unless,
in some shape or other, we introduce them all. A man takes
mercury, goes out of doors, and catches cold. We say, perhaps,
that the cause of his taking cold was exposure to the air. It is
clear, however, that his having taken mercury may have been a
necessary condition of his catching cold; and though it might
consist with usage to say that the cause of his attack was exposure
to the air, to be accurate we ought to say that the cause was
exposure to the air while under the effect of mercury.

"If we do not, when aiming at accuracy, enumerate all the
conditions, it is only because some of them will, in most cases, be
understood without being expressed, or because for the purpose in
view they may, without detriment, be overlooked. For example,
when we say, the cause of a man's death was that his foot slipped
in climbing a ladder, we omit, as a thing unnecessary to be stated,
the circumstance of his weight, though quite as indispensable a
condition of the effect which took place."

" In all these instances the fact which was dignified by the
name of cause, was the one condition which came last into exist-
ence. But it must not be supposed that in the employment of the
term, this or any other rule is always adhered to. Nothing can
better show the absence of any scientific ground for the distinc-
tion between the cause of a phenomenon and its conditions, than
the capricious manner in which we select from among the condi-
tions that which we choose to denominate the cause. However
numerous the conditions may be, there is hardly any of them
which may not, according to the purpose of our immediate
discourse, obtain that nominal pre-eminence." ^

" Thus we see that each and every condition of the phenomenon
may be taken in its turn, and with equal propriety in common
parlance, but with equal impropriety in scientific discourse, may be

1 Logic, pp. 237, 238.

8o Inductive Logic.

spoken of as if it were the entire cause. And in practice that
particular condition is usually styled the cause whose share in the
matter is superficially the most conspicuous, or whose requisite-
ness to the production of the effect we happen to be insisting
upon at the moment. So great is the force of this last considera-
tion, that it often induces us to give the name of cause even to
one of the negative conditions. We say, for example, the cause
of the army's being surprised was the sentinel's being off his post.
But since the sentinel's absence was not what created the enemy,
or made the soldiers to be asleep, how did it cause them to be
surprised ? All that is really meant is, that the event would not
have happened if he had been at his duty. His being off his post
was no producing cause, but the mere absence of a preventing
cause : it was simply equivalent to his non-existence. From
nothing, from a mere negation, no consequences can proceed.
All effects are connected, by the law of causation, with some set
of positive conditions; negative ones, it is true, being almost
always required in addition. In other \vords, every fact or
phenomenon which has a beginning, invariably arises when some
certain combination of positive facts exists, provided certain other
positive facts do not exist." ^

" The cause, then, philosophically speaking, is the sum total of
the conditions, positive and negative, taken together; the whole of
the contingencies of every description, which being realized, the
consequent invariably follows." ^

In this great definition Mr. Mill provides for no
effects but events, and for no causes but complexes of
things, of collocations, and of history.

" The state of the whole universe at any instant, we believe to
be the consequence of its state at the previous instant : insomuch
that one who knew all the agents which exist at the present
moment, their collocation in space, and all their properties, in other
words, the laws of their agency, could predict the whole subsequent
history of the universe, at least unless some new volition of a
power capable of controlling the universe should supervene." ^

1 Logic, p. 239. 2 ibid.^ p. 241. 3 jbid.^ p. 250.

Mr. Mill's Doctrme of Causation. 8i

The cause of the heating of the water in Count
Rumford's box, then, and the only thing to which
a philosopher can give the name of cause, was the
immediately previous state of the universe. And
what we have learned from the experiment is the in-
variable and unconditional succession between that
state of the universe and the heating of just such a box
of water. But since the universe never was before in
just that state, and never will be again, it is hard to see
that we have learned anything at all. Mr. Mill refuses
to recognize any difference in the relations of the dif-
ferent sorts of causes to the event. "All the positive
conditions of a phenomenon are alike agents, alike
active." ^

Although it was with the notion of succession that
Mr. Mill began his definition of cause, yet he did not
hold to it with great firmness. He inquires : —

" Does a cause always stand with its effect in the relation of
antecedent and consequent? Do we not often say of two simul-
taneous facts that they are cause and effect — as when we say
that fire is the cause of warmth, the sun and moisture the cause of
vegetation, and the like? Since a cause does not necessarily
perish because its effect has been produced, the two, therefore, do
very generally coexist ; and there are some appearances, and some
common expressions, seeming to imply not only that causes may,
but that they must, be contemporaneous with their effects.
Cessante causa, cessat et effectiis, has been a dogma of the
schools : the necessity for the continued existence of the cause in
order to the continuance of the effect, seems to have been once
a general doctrine among philosophers. Kepler's numerous
attempts to account for the motion of the heavenly bodies on
mechanical principles, were rendered abortive by his always sup-

1 Logic, p. 243.

82 Inductive Logic.

posing that the force which set those bodies in motion must
continue to operate in order to keep up the motion which it at
first produced. Yet there were at all times many familiar in-
stances in open contradiction to this supposed axiom. A coup de
soleil gives a man a brain fever : will the fever go off as soon as
he is moved out of the sunshine ? A sword is run through his
body : must the sword remain in his body in order that he may
continue dead 1 A ploughshare once made, remains a plough-
share, without any continuance of heating and hammering, and
even after the man who heated and hammered it has been gath-
ered to his fathers. On the other hand, the pressure which
forces up the mercury in an exhausted tube must be continued in
order to sustain it in the tube. This (it may be replied) is
because another force is acting without intermission, the force
of gravity, which would restore it to its level, unless counterpoised
by a force equally constant. But again : a tight bandage causes
pain, which pain will sometimes go off as soon as the bandage is
removed. The illumination which the sun diffuses over the earth
ceases when the sun goes down.

" There is therefore a distinction to be drawn. The conditions
which are necessary for the first production of a phenomenon, are
occasionally also necessary for its continuance; but more com-
monly its continuance requires no conditions except negative
ones. Most things, once produced, continue as they are, until
something changes or destroys them; but some require the perma-
nent presence of the agencies which produced them at first. These
may, if we please, be considered as instantaneous phenomena,
requiring to be renewed at each instant by the cause by which
they were at first generated. Accordingly, the illumination of any
given point of space has always been looked upon as an in-
stantaneous fact, which perishes and is perpetually renewed as
long as the necessary conditions subsist. If we adopt this lan-
guage, we are enabled to avoid admitting that the continuance of
the cause is ever required to maintain the effect. We may say, it
is not required to maintain, but to reproduce the effect, oi else to
counteract some force tending to destroy it. And this may be a
convenient phraseology. But it is only a phraseology. The fact
remains that in some cases (though these are a minority) the con-

Mr. Mill's Doctrine of Causation. 83

tinuance of the conditions which produced an effect is necessary
to the continuance of the effect.

" As to the ulterior question, whether it is strictly necessary
that the cause, or assemblage of conditions, should precede, by
ever so short an instant, the production of the effect (a question
raised and argued with much ingenuity by a writer from whom
we have quoted), we think the inquiry an unimportant one.
There certainly are cases in which the effect follows without an
interval perceptible to our faculties ; and when there is an interval,
we cannot tell by how many intermediate lines imperceptible to
us that interval may really be filled up. But even granting that
an effect may commence simultaneously with its cause, the view
I have taken of causation is in no way practically affected.
Whether the cause and its effect be necessarily successive or not,
causation is still the law of the succession of phenomena. Every-
thing which begins to exist must have a cause; what does not
begin to exist does not need a cause; what causation has to
account for is the origin of phenomena, and all the successions of
phenomena must be resolvable into causation. These are the
axioms of our doctrine. If these be granted, we can afford,
though I see no necessity for doing so, to drop the words ante-
cedent and consequent as applied to cause and effect. I have no
objection to define a cause, the assemblage of phenomena, which
occurring, some other phenomenon invariably commences, or has
its origin. Whether the effect coincides in point of time with, or
immediately follows, the hindmost of its conditions, is immaterial.
At all events it does not precede it ; and when we are in doubt,
between two coexistent phenomena which is cause and which
effect, we rightly deem the question solved if we can ascertain
which of them preceded the other." ^

This admission cannot but be regarded as most
damaging for the definition. Mr. Mill's confusion here
arises from not having discriminated the various senses
of the words cause and effect, and from not having dis-
tinguished between matter, energy, persons, events,

1 Logic, pp. 247, 248.

84 Inductive Logic.

states, and historical concatenations which are mere
sequences of possibilities. The effects which Mr. Mill
finds following their causes are states; the effects
which are simultaneous with their causes are events.
When a ball is struck, the motion of the bat passes into
it; that effect is simultaneous. But the state of motion
once begun continues indefinitely ; this effect there-
fore follows its cause, the blow. Strictly speaking, the
cause of an event cannot precede that event. Count
Rumf ord existed, it is true, before his experiment ; and
in that sense the cause preceded the effect. But, when
living under the name of Benjamin Thompson in Con-
necticut, he was in no proper sense the cause of the
experiment years later in Munich. He might have
been slain in the war of the Revolution and never
have gone to Munich at all. He was not really the
cause of the experiment until he performed it. Things
exist permanently, and of course both precede and
follow their effects. Particular events are always
simultaneous with their causes, the things that react.
States continue indefinitely after the events that intro-
duce them. Events in history precede the events for
which they open the way, and of which they are there-
fore called the causes.

Mr. Mill says: "The law of Causation, the recogni-
tion of which is the main pillar of inductive science, is
but the familiar truth that invariability of succession is
found by observation to obtain between every fact in
nature and some other fact which has preceded it."
But this language is exceedingly liable to mislead a
hasty reader into thinking that Mr. Mill means to say
that each particular fact has some other particular fact

Mr. Mill's Doctrine of Causation. 85

as its cause. " It is seldom, if ever, between a con-
sequent and a single antecedent, that this invariable
sequence subsists." In truth, the facts between which
Mr. Mill asserts invariability of succession are states
of the universe. "The cause," he says, "is the sum
total of the conditions, positive and negative, taken
together ; the whole of the contingencies of every
description." "The state of the whole universe at
any instant, we believe to be the consequence of its
state at the previous instant."

Mr. Mill understands his definition to mean that the
cause is the sum total of the conditions "immediately,
not remotely, preceding the effect." But it is hard to
reconcile this interpretation with the explanations which
place historical events among the antecedents. If
taking mercury and subsequently being exposed to the
air are among the conditions of a man's death, the
cause cannot be the total of the immediately antecedent
conditions. Mr. Mill escapes the difficulty by saying,
that remote events are conditions of the conditions ;
they are not the causes, but the causes of the causes ;
or rather factors of the causes of factors of the cause.

Mr. Mill felt that there must be something in causa-
tion more than mere invariable succession. There
must be something which other writers had attempted
to express by the term necessity, and for this he
'selected the word unconditionalness . He says : —

"Jf there be anything which confessedly belongs to the term
necessity, it is uncojiditionalness. That which is necessary, that
which 7nust be, means that which will be, whatever supposition we
may make in regard to other things. The succession of day and
night evidently is not necessary in this sense. It is conditional

S6 Inductive Logic.

on the occurrence of other antecedents. That which will be fol-
lowed by a given consequent when, and only when, some third
circumstance also exists, is not the cause, even though no case
should ever have occurred in which the phenomenon took place
without it." 1

Returning to the definition, we find the cause to be
the antecedent or concurrence of antecedents, that is, a
complex ; but a complex of what } Of conditions, all
equally essential. It is the assemblage that constitutes
the particular cause. When we are told that the con-
sequent must be unconditionally consequent upon the
assemblage of these conditions, what is that but to
learn that the assemblage of conditions must lack no
condition, that is, must be complete t What Mr. Mill
wanted to say was that no superfluous circumstance,
nothing that does not have some efficiency, must be
counted among the conditions. But since, according to
his doctrine, the cause, philosophically viewed, is the
immediately previous state of the universe, and since
inductive science knows nothing about efficiency, this
is difficult to avoid.

Let us revert, parenthetically, to the question whether
day is the cause of night, and night the cause of day.
This question illustrates the necessity of an analysis of
terms before beginning to discuss about facts. All
light is not day, nor is all darkness night. The
darkness in the Mammoth Cave is not night, nor is
the illumination of the cave, by the combustion of
magnesium, day. A day is that portion of the sun's
illumination which is cut off and individualized by two
nights. As soon as this is stated, it is seen that night

1 Logic, p. 245.

Mr. Mill's Doctrine of Causation. Sy

is the cause of day. At the north pole there is but
one day in the year, because there is but one night.
But in what sense is night the cause of day ? It is not
the efficient cause, nor the material cause, nor the
conditional cause, but simply the historical cause. The
event, an interruption of light by rotation, makes a
possibility for a restoration of light by rotation. If one
event did not occur, the other could not occur ; the
occurrence of night is an essential condition of the
occurrence of day.

Mr. Mill holds that the actions of the Will are under
exactly the same laws of causation as the reactions of
matter. He says : —

" The question, whether the law of causality applies in the same
strict sense to human actions as to other phenomena, is the cel-
ebrated controversy concerning the freedom of the will ; which,
from at least as far back as the time of Pelagius, has divided both
the philosophical and the religious world. The affirmative opinion
is commonly called the doctrine of Necessity, as asserting human
volitions and actions to be necessary and inevitable. The negative
maintains that the will is not determined, like other phenomena,
by antecedents, but determines itself ; that our volitions are not,
properly speaking, the effects of causes, or at least have no causes
which they uniformly and implicitly obey.

" I have already made it sufficiently apparent that the former of
these opinions is that which I consider the true one ; but the mis-
leading terms in which it is often expressed, and the indistinct
manner in which it is usually apprehended, have both obstructed
its reception, and perverted its influence when received. The
metaphysical theory of free will, as held by philosophers (for the
practical feeling of it, common in a greater or less degree to all
mankind, is in no way inconsistent with the contrary theory), was
invented because the supposed alternative of admitting human
actions to be necessary, was deemed inconsistent with every one's
instinctive consciousness, as well as humiliating to the pride and

88 Inductive Logic.

even degrading to the moral nature of man. Nor do I deny that
the doctrine, as sometimes held, is open to these imputations ; for
the misapprehension in which I shall be able to show that they
originate, unfortunately is not confined to the opponents of the
doctrine, but participated in by many, perhaps we might say by
most of its supporters.

" Correctly conceived, the doctrine called Philosophical Neces-
sity is simply this : that, given the motives which are present to
an individual's mind, and given likewise the character and disposi-
tion of the individual, the manner in which he will act may be
unerringly inferred ; that if we knew the person thoroughly, and
knew all the inducements which are acting upon him, we could
foretell his conduct with as much certainty as we can predict any
physical event. This proposition I take to be a mere interpretation
of universal experience, a statement in words of what every one
is internally convinced of. No one who believed that he knew
thoroughly the circumstances of any case, and the characters of
the different persons concerned, would hesitate to foretell how all
of them would act. Whatever degree of doubt he may in fact
feel, arises from the uncertainty whether he really knows the
circumstances, or the character of some one or other of the
persons, with the degree of accuracy required ; but by no means
from thinking that if he did know these things, there could be any
uncertainty what the conduct would be. Nor does this full
assurance conflict in the smallest degree with what is called our
feeling of freedom. We do not feel ourselves the less free,
because those to whom we are intimately known are well assured
how we shall will to act in a particular case. We often, on the
contrary, regard the doubt what our conduct will be, as a mark of
ignorance of our character, and sometimes even resent it as an
imputation. It has never been admitted by the religious philos-
ophers who advocated the free-will doctrine, that we must feel not
free because God foreknows our actions. We may be free, and
yet another may have reason to be perfectly certain what use we
shall make of our freedom. It is not, therefore, the doctrine that
our volitions and actions are invariable consequents of our ante-
cedent states of mind, that is either contradicted by our conscious-
ness, or felt to be degrading.

Mr. Mill's Doctrine of Causation. 89

"But the doctrine of causation, when considered as obtaining
between our voHtions and their antecedents, is almost universally-
conceived as involving more than this. Many do not believe, and
very few practically feel, that there is nothing in causation but
invariable, certain, and unconditional sequence. There are few to
whom mere constancy of succession appears a sufficiently stringent
bond of union for so peculiar a relation as that of cause and effect.
Even if the reason repudiates, imagination retains, the feeling of
some more intimate connection, of some peculiar tie, or mysterious
constraint exercised by the antecedent over the consequent. Now
this it is which, considered as applying to the human will, conflicts
with our consciousness, and revolts our feelings. We are certain
that, in the case of our volitions, there is not this mysterious
constraint. We know that we are not compelled, as by a magical
spell, to obey any particular motive. We feel, that if we wished
to prove that we have the power of resisting the motive we could
do so (that wish being, it needs scarcely be observed, a new
antecedenf)^ and it would be humiliating to our pride, and paralyz-
ing to our desire of excellence, if we thought otherwise. But
neither is any such mysterious compulsion now supposed, by the
best philosophical authorities, to be exercised by any cause over
its effect. Those who think that causes draw their effects after
them by a mystical tie, are right in believing that the relation
between voHtions and their antecedents is of another nature. But
they should go farther, and admit that this is also true of all other
effects and their antecedents. If such a tie is considered to be
involved in the word Necessity, the doctrine is not true of human
actions ; but neither is it then true of inanimate objects. It would
be more correct to say that matter is not bound by necessity, than
that mind is so." ^

Mr. Mill escapes " the depressing effect of the fatalist
doctrine " by saying that, while we must will as our
character is, we can, if we desire, place ourselves in
different circumstances, and these will work in us a
different character, and then we shall will differently.

1 Logic, pp. 581, 582.

90 Inductive Logic.

That is, our history having been what it has, we cannot
will differently from what we do, but we can wish to
will differently. But this is to suppose the same cause
producing simultaneously a will in one direction and a
wish in the other direction, — the same fountain send-
ing forth sweet water and bitter. Mr. Mill says that
"human actions are never ruled by any one motive
with such absolute sway that there is no room for the
influence of any other. The causes, therefore, on
which an action depends are never uncontrollable."
But it is precisely the characteristic of causation in
physics that there is never an alternative unless some
will intervenes. If human actions are never absolutely
ruled by one motive, they differ from the reactions of
matter, which are absolutely ruled in each case by one
cause.

The conviction made by a careful examination of
Mr. Mill's doctrine of Causation is, that it lacks
in clearness and self-consistency, and that it is
an inadequate basis for the whole superstructure of
Inductive Logic.

CHAPTER XI.
CANONS FOR ISOLATING FACTS OF CAUSATION.

It is one task of Science, amid the crowd of phe-
nomena, to distinguish between the coexistences ♦and
successions which are accidental and those which rest
upon real relations. For it is only by such knowledge
that man can live among the terrific forces of nature
and can make them the servants of his will. There
are many groups of phenomena of which it may be
known that when one is present, the others are present
also. They are permanent coexistences. There are
many events of which it may be known that when one
has happened, the other or the others will be sure to
follow. There is said to be a relation of causation
between them. We have already, at great length, dis-
cussed the word cause. An event is the reaction of
certain substances and energies in a certain collocation.
The reaction by which this collocation arose, or any
previous reaction in the long line of history, is an his-
torical cause of the event. This total of things,
including the collocation, which is their mutual relation
in space, and including their history in time, may be
called the Comprehensive Cause of the event, and also
of the things in their states after the event. '

Events are the actions of things. But every action
is a reaction. This is a primary induction which men
were long in making. The law of inertia, that every
body remains in its state of rest or motion until acted

g2 Inductive Logic.

upon, is a subordinate generalization: the wider law is
that it takes at least two to make, not only a bargain
or a quarrel, but anything. This is often what is
understood to be meant by the law of causation; and
it seems to be regarded as intuitively known. But it
is really an induction.

If we can isolate two things so that we are sure
that no third is present, and if then an event occurs,
we are sure that it is a reaction between those two
things. When a bit of glowing iron is lowered into a
jar of oxygen and vivid combustion follows, we are
sure that the iron and the oxygen are reacting; those
two things are the sole material causes of the event.
When a feather and a gold coin are supported in an
exhausted receiver and then by the turn of a screw are
left unsupported, we know that they are free from all
particular influences and are reacting with the general
mass of things as a whole : the fall therefore is caused
by that reaction alone. This general reaction is called
gravitation.

It is plain that the presence of a third thing destroys
the isolation and leaves us in doubt. The combustion
of a bit of iron in common air, where nitrogen is
present, could not be known, without investigation, to
be a reaction of the iron and oxygen alone. It might
be a mutual reaction of all three or a reaction of
the iron and the nitrogen. But so crowded is the
world with things, and so multitudinous are their
reactions, that it is a rare good fortune to be able
mechanically to separate a pair or a group of reagents.
What cannot be done physically must be done in
thought. We must make a mental elimination, or

Cations for Isolating Facts of Causation. 93

perhaps a series of eliminations, and thus discover the
various reagents that enter into the comprehensive
cause of any event that may be in question. These
eliminations are made in thought by the process of
subtraction.

Canon First.

FOR ISOLATING FACTS OF CAUSATION BY THE TEST OF
DIFFERENCE.

In any two instances^ the circumstances which are not
common are the causes of the events which are not
common.

This brief and general language requires explanation.
By an instance is meant any group of phenomena
which may be under investigation. By a circumstance
is meant a substance, an energy, a will, a collocation,
or a previous event. Consequently the cause dis-
covered may be the material cause, the energetic cause,
the conditional cause, the volitional cause, or the his-
torical cause — the mere occurrence of the possibility
of the reaction of the efficient causes. What is dis-
covered is far more likely to be merely one factor of
one of these causes than to be the whole of it ; there-
fore, to avoid the tediousness of constantly saying
"at least a part of one of the causes," we will adopt
the name Empirical Cause. The circumstance dis-
covered by this method is what ordinary experience
leads unscientific people to speak of as the cause;
and this crude use of experience is what is called
empiricism.

The validity of this canon is obvious. Since events
are the reactions of things, whatever is different in the

94 Inductive Logic.

events must come from differences in the things, or in
their collocations, which afford the possibilities of
reaction. But differences in collocation arise through
events. Thus the whole of the differences in two
groups of phenomena must be accounted for by the
things, their collocations, and their history. Let us
consider a concrete example. In a dark room some
one touches a button, and immediately a brilliant
illumination follows. There are here two instances,
the room in darkness and the room illuminated.
Viewed historically, the difference in circumstances is
that the one instance includes the previous event of
the touch of the button and the other does not. The
touch of the button is therefore the historical cause of
the illumination. But leaving out of view the history,
it will be found that the two instances differ in the col-
location of things. In the one case materials are so
disposed that there is no continuous circuit for the
electricity and in the other case there is a continuous
circuit. Here is found the conditional cause. Fur-
ther, the two instances differ, in that in one the
electricity passes and in the other it does not ; hence
we discover the energetic cause, which is the elec-
tricity. By thus confining the attention successively
to the history, the materials, the energy, or the con-
ditions, the several kinds of cause may be elicited.
Under this canon four cases may arise: — ^"
Case I. On striking the balance between circum-
stances and events in the two instances, a single
circumstance and a single event may be left, hot com-
mon to both instances. If so, that circumstance is
manifestly the empirical cause of that event. If, for

Canons for Isolating Facts of Causation. 95

example, into a glass containing some dilute sulphuric
acid a few bits of marble be dropped, vigorous ebul-
lition will ensue. The glass containing the acid, as it
was before the dropping in of the marble, constitutes
one instance; the same glass containing the marble in
addition to the acid constitutes the second instance.
Historically viewed, the only difference is that the one
instance includes the previous event of the dropping in
of the bits of marble; this therefore is the historical
cause. But viewed materially, the sole difference is in
the bits of marble, which were absent at first and
afterwards present. The marble is therefore the
material cause of the ebullition. But it is only the
empirical material cause; it is not the comprehensive
material cause, for in that the acid is as important a
factor as the marble. When there are a number of
things present and a new factor is introduced, we can-
not tell by a single application of the canon how many
of them co-operate with that new factor in a new com-
prehensive cause.

Case 2. On striking the balance, a group of circum-
stances and a group of events may be left not common
to the two instances. If so, those circumstances are
the empirical causes of those events, but which are the
causes of which, can be ascertained only by a further
application of the canon to simpler instances. For
example, Daniel Webster left the paternal farm and,
after spending four years in Dartmouth College,
graduated as an accomplished orator. The two
instances are Webster without education and without
eloquence, and Webster after his college education,
delivering some eloquent oration. The two instances

96 Inductive Logic.

differ in the group of circumstances constituting a
college education. But this group is very complex, so
that, while it is plain that among the circumstances
are included the empirical causes of polished eloquence,
it is not plain whether any particular circumstance, as
the study of the Greek and Roman classics, was in
any sense a cause. Indeed, it may have been a
hindrance.

Case J. On striking the balance, the difference may
be found to be, that in the first instance there is more
of one circumstance and more of one event than in the
second instance. This case is but a variety of the
first ; for an additional quantity is a new circumstance
or a new event. For example, a youth ambitious for
athletic honors may, by careful training, wonderfully
increase his muscular strength. He has always taken
some care of his health, and a little natural superiority
may be that which awakens his ambition ; but with
more care comes more power. Here the added care is
a new circumstance and the addition of strength is a
new event.

Case /f.. On striking the balance, the difference may
be found to be that in the first instance there is more
of several circumstances and more of several events,
the kinds remaining unchanged. This is merely a
variety of Case 2 ; for the new quantities are new
circumstances and new events. For example, after
taking the Bachelor's degree, one may go on another
year and take the Master's degree. He will become a
more learned person, but we do not know any better
than before, which of his studies have contributed to
the group of results included in an education.

Canons for Isolating Facts of Causation. 97

These four cases may be expressed in symbols as
follows : —

I. ABC def 2. ABCD efgh 3. AABC ddef 4. AABCDD efghh
BC ef BC fg ABC def ABCD efgh

A d A D e h A d A D e h

Let capital letters represent circumstances and
small letters represent events. On striking the bal-
ance in Case i, the single circumstance A and the
single event d are found not common. Since what is
not common in the events must be owing to what is
not common in the circumstances, A must be the
empirical cause of d. In Case 2, A and D are not
common among the circumstances, and e and h are not
common among the events. A and D include, there-
fore, the causes of e and h; but which is the cause of
which, or whether one is inert and the other is the
cause of both events, we cannot say. We must find
another instance presenting A without D before we
can make a further isolation. Case 3 gives the same
result as Case i, and Case 4 gives the same result
as Case 2.

In the first case, as soon as we find the instance
ABC def, we know that those circumstances are the
causes of those events; for, unless we are sure that
there are no other significant circumstances and events,
we have not found the instance at all. Just so, as
soon as we find the instance BC ef, we know that
those circumstances are the causes of those events.
We make these affirmations on the basis of the primary
induction that all of the events in the world are the
reactions of things in the collocations which permit
those reactions. Therefore we know that A, the

98 Inductive Logic.

circumstance in which the two instances differ, is the
empirical cause of dy the event in which they differ.
But it often happens that we can find no single
instance BC ef, although we may know from previous
observations that B is the cause of e and that C is the
cause of /. This makes no difference in the reasoning
or in the result. However the knowledge that B and
C cause e and / has been obtained, we make the same
use of it ; we subtract from the totals in the first in-
stance those circumstances and events whose relations
are already known, and the remaining circumstances
and events are then known to be mutually related, or
we know at least that among the circumstances are the
causes of all the events not common. The same
remark may be made mutatis mutandis of the three
other cases.

From the establishment of a single fact of causation
we pass easily to a generalization. The primary
inductions, that things persist, and that the qualities of
things persist, are already made. What a thing causes
once, it always causes under the same conditions.
Therefore, after isolating a single fact of causation, we
are warranted in the secondary induction, that the cir-
cumstance, under the same conditions, will always
cause the given event.

The test of difference, when two good instances can
be found or artificially produced, is quick and decisive.
In the experiment of Count Rumford, it was easy to
compare the apparatus when the water was cold and
when the water was hot. It was easy also to see that
the only circumstance in which the two instances
differed was the motion of the cylinder. The event.

Canons for Isolating Facts of Causation. 99

the heating, was therefore undoubtedly attributable to
that circumstance as empirical cause. But it is not
always possible to apply this canon, and then our only
resource is one far less satisfactory.

Canon Second.

FOR ISOLATING FACTS OF CAUSATION BY THE TEST OF
A GREEMENT.

If in two instances the same event occurs, the common
circumstances probably include the cause ; and the proba-
bility rapidly increases with the member and variety of
the instances.

The word cause here still means merely empirical
cause. Inexact as this test is, it is often our only expe-
dient, and with care it is highly useful. For example, if
twice after the imposition of a protective tariff, business
is seen to flourish, a slight probability arises that the
tariff is the cause of the prosperity. Yet there is a
possibility in each case that some other circumstance,
as unusual harvests, or discoveries of rich deposits of
the precious metals, may have been the cause. Indeed,
the only effect of the tariff may have been to diminish
somewhat each time the total prosperity. But every
instance in which a tariff is accompanied by prosperity
rapidly increases the probability of a genetic connec-
tion ; since otherwise we must suppose the fortuitous
occurrence of some other beneficent cause every time
Congress happens to be in favor of protection.

The argument from the test of agreement often
seems stronger than it is, from our unconsciously
blending it with the argument from the test of differ-

lOO IndtLctive Logic.

ence. In the case of prosperity after the imposition of
a tariff, we naturally compare the country as it was
before the tariff and as it was soon after, and thus
apply the test of difference ; but this gives to the argu-
ment from agreement an appearance of strength not
its own.

It must be observed that, in the canon, the common
circumstances are said simply to include, not necessa-
rily all to be, the cause. The ashes of seaweeds were
long known to possess valuable medicinal powers.
The use of them in certain diseases was followed by
beneficial effects. But it was not known which of the
ingredients was efficient or whether all were efficient ;
all were common circumstances, but some might be
always inert, and some might even be obstructive.
Later it was discovered that the useful substance was
nothing but iodine ; the other things were better away.

As an illustration of how the test of agreement may
be applied, with some admixture of the test of differ-
ence, we will quote an eloquent passage from Schiller's
y^sthetical Essays : —

" It is certainly a matter entitled to reflection that, at almost
all the periods of history when art flourished and taste held sway,
humanity is found in a state of decline ; nor can a single instance
be cited of the union of a large diffusion of aesthetic culture with
political liberty and social virtue, of fine manners associated with
good morals, and of politeness fraternizing with truth and loyalty
of character and life. As long as Athens and Sparta preserved
their independence, and as long as their institutions were based
on respect for the laws, taste did not reach its maturity, art
remained in its infancy, and beauty was far from exercising her
empire over minds. No doubt, poetry had already taken a
sublime flight, but it was on the wings of genius, and we know

Canons for Isolating Facts of Causation. loi

that genius borders very closely on savage coarseness, that it is a
light which shines readily in the midst of darkness, and which,
therefore, often argues against, rather than in favor of, the taste of
the time. When the golden age of art appears under Pericles and
Alexander, and the sway of taste becomes more general, strength
and liberty have abandoned Greece ; eloquence corrupts the truth,
wisdom offends it on the lips of Socrates, and virtue in the life of
Phocion. It is well known that the Romans had to exhaust their
energies in civil wars, and, corrupted by Oriental luxury, to bow
their heads under the yoke of a foreign despot, before Grecian art
triumphed over the stiffness of their character. The same was the
case with the Arabs : civihzation only dawned upon them when
the vigor of their military spirit became softened under the
Abbassides. Art did not appear in modern Italy till the glorious
Lombard league was dissolved, Florence submitting to the Medici,
and all those brave cities gave up the spirit of independence for
an inglorious resignation. It is almost superfluous to call to
mind the example of modern nations, with whom refinement has
increased in direct proportion to the decline of their liberties.
Wherever we direct our eyes in past times, we see taste and free-
dom mutually avoiding each other. Everywhere we see that the
beautiful only founds its sway on the ruins of heroic virtues." ^

Under this canon three cases may arise, represented
by symbols as follows : —

I. ABC def 2. ABC def 3. ABC def

APE dgh ABE deg AFG deh

A d AB de A de

In the first case there is one common event and one
common circumstance. In the second case there is a
group of common events and a group of common cir-
cumstances. In the third case there is a single
common circumstance but a group of common events.

This third case suggests a remark, vi^hich should be
made also regarding the others. A serious element of

^ Bohn's Trans., p. 55.

102 Inductive Logic.

uncertainty weakens the test of agreement, and that is
what is called the Plurality of Causes. What is appar-
ently the same event may be caused by different
things. Light -may be made by electricity or by com-
bustion. The canon asserts no more than that the
common circumstances probably include the cause.
Even in Case i, A^ the only common circumstance,
may not be the cause of </, the only common event ;
for B may be the cause of d in the first instance and D
may be the cause of d in the second. A may be wholly
inert in both instances. It is only when a number of
instances have been observed that confidence finds
much basis. Ebullition may occur in hydrochloric
acid, and yet all the common circumstances may be
irrelevant, for marble may be the cause in one instance
and zinc may be the cause in the second. In Case 3,
A may be the cause of d and some other circumstance
may each time cause e.

CHAPTER XII.

MR. MILL'S FOUR EXPERIMENTAL METHODS.

To Mr. Mill is due the credit of first distinctly
formulating and elaborately discussing the methods of
isolating facts of causation. His treatment of the sub-
ject has powerfully influenced all subsequent writers,
and his terminology has entered into the general
vocabulary of philosophy. It is, therefore, necessary
for the student to understand these, if he would under-
stand the current literature of inductive logic.

Mr. Mill treats of the tests which we have discussed
in the last chapter, under the heading, " The Four
Experimental Methods." He recognizes, indeed, that
fundamentally there are but two, and says : —

" The simplest and most obvious modes of singling out from
among the circumstances which precede or follow a phenomenon,
those with which it is really connected by an invariable law, are
two in number. One is, by comparing together different instances
in which the phenomenon occurs. The other is, by comparing
instances in which the phenomenon does occur, with instances in
other respects similar in which it does not. These two methods
may respectively be denominated the Method of Agreement and
the Method of Difference." i

For the application of these methods Mr. Mill pro-
ceeds to formulate five canons, as follows : —

1 Logic, p. 278.

104 Inductive Logic.

First Canon.

For the Method of Agreement,

If two or more instances of the phenomenon under investiga-
tion have only one circumstance in common, the circumstance in
which alone all the instances agree, is the cause (or effect) of the
given phenomenon.

Second Canon.

For the Method of Difference.

If an instance in which the phenomenon under investigation
occurs, and an instance in which it does not occur, have every
circumstance in common save one, that one occurring only in the
former ; the circumstance in which alone the two instances differ,
is the effect, or the cause, or an indispensable part of the cause,
of the phenomenon.

Third Canon.

For the foint Method of Agree7nent and Difference; or the
Indirect Method of Difference.

If two or more instances in which the phenomenon occurs have
only one circumstance in common, while two or more instances in
which it does not occur have nothing in common save the absence
of that circumstance ; the circumstance in which alone the two
sets of instances differ, is the effect, or cause, or an indispensable
part of the cause, of the phenomenon.

Fourth Canon.

For the Method of Residues.

Subduct from any phenomenon such part as is known by previ-
ous inductions to be the effect of certain antecedents, and the
residue of the phenomenon is the effect of the remaining antece-
dents.

Mr. Mill's Four Experhnental Methods. 105

Fifth Canon.
For the Method of Conco7niiant Variations.

Whatever phenomenon varies in any manner whenever another
phenomenon varies in some particular manner, is either a cause or
an effect of that phenomenon, or is connected with it through
some fact of causation. '

vUpon these methods we remark : —

I. The name "The Four Experimental Methods"
is of doubtful propriety. The methods are confessedly
in principle but two ; and the canons are five. But
Mr. Mill fixed upon the number four because he did
not regard the method of Residues as strictly inductive.
The method of Residues provides for those instances
of the application of the method of Difference which
we have discussed under Case i of our Canon i, on
page 98, in which, instead of subtracting a single
instance, we subtract the sum of several instances, in
order to make the isolation. The fact that in such
cases the subtrahend is composite, made by an addition
of simpler instances, leads Mr. Mill to formulate a
special canon and to declare it deductive. He is not
always of the same mind regarding the method of
Residues ; since he says, " By previous inductions we
have ascertained the causes of some of these effects," ^
meaning those which are added together to make the
compound subtrahend ; but he says later, " It concludes
not from a comparison of instances, but from the
comparison of an instance with the result of a previous
deduction.'" ^

1 Logic, p. 284. 2 /bid,^ p. 613.

io6 Inductive Logic.

The method of Residues and the method of Differ-
ence are, however, identical in principle. The rare
word "subduct," which Mr. Mill employs, means only
"take .the difference," and a "residue" is nothing but
a "difference." The single step of addition cannot

make the difference between induction and deduction.

Mr. Mill says, " The Method of Residues is in truth a
peculiar modification of the Method of Difference,"
and again, " The Method of Residues, as we have seen,
is not independent of deduction ; though, as it also
requires specific experience, it may, without impro-
priety, be included among methods of direct observation
and experiment." This remark implies that Mr. Mill
regarded the other methods as entirely independent of
deduction. Still he says . of the two fundamental
methods, "Both are methods of elimination." But
elimination is a purely deductive process. Mr. Mill
did not see that deductive logic covers the whole field
of induction, that his methods only served to isolate
single facts, and that he then combined those facts,
directly in making a primary induction, or in a syllogism
with some primary induction already made, to get some
general truth as a secondary induction. He has told
us these things in detached portions with great clear-
ness, but he never put them together. Mr. Mill seems
to think that his methods give us general truths
immediately. But facts isolated by these methods
have no more inductive significance than other single
facts which need no artificial isolation.

In attempting to use the test of difference, we may
discover that we have not accurately stated our
instances. For example, we may think that we have

Mr. Mill's Four Experimental Methods. loy

observed the two instances BC def and BC ef.
But upon comparison it appears that while the causes
observed in both instances are the same, there is an
effect in one which is not in the other. This shows
that we must have overlooked a cause, and puts us
upon a search for it. Mr. Mill sometimes seems to
regard this correction of instances as a use of the
method of residues. He quotes with approval the
language of Whewell, " Many of the new elements of
chemistry have been detected in the investigation of
residual phenomena. Thus Arfwedson discovered
lithia by perceiving an excess of weight in the sulphate
produced from a small portion of what he considered
as magnesia present in a mineral he had analyzed."
But this correction of instances is just as likely to
occur in using the simple method of difference as in
using the method of residues. There is no necessary
connection between the correction of instances and
the use of a compound subtrahend, which is the char-
acteristic of the method of residues.

The term " experimental " is even less defensible
than the number four. For Mr. Mill says : " Of these
methods, that of Difference is more particularly a
method of experiment ; while that of Agreement is
more especially the resource employed where experi-
ment is impossible." If it is employed especially
where experiment is impossible, some name should be
found more appropriate than " experimental."

2. Mr. Mill does not seem aware of the vagueness
of the terms and results of his canons. In his chapter
on the Law of Causation, he says, "The cause then,
philosophically speaking, is the sum total of the condi-

io8 Inductive Logic,

tions positive and negative taken together, the whole
of the contingencies of every description, which being
realized, the consequent invariably follows." But the
methods never isolate a cause in this sense ; it is only
the empirical cause — some single factor or group of
factors. It is, therefore, superfluous to say in the
second and third canons " the cause or an indispensable
part of the cause."

Mr. Mill regarded succession as essential in the
notion of causation, and, illustrating the methods by
letters of the alphabet, he says, "We shall denote
antecedents by large letters of the alphabet, and the
consequents corresponding to them by the small."
Yet in only one of the canons does he make any refer-
ence to sequence. Indeed, he makes them so general
that the conclusion may be that the "circumstance"
is either the cause or the effect of the phenomenon.
This failure to hold fast the idea of sequence leads to
curious results. Take the following illustration of the
method of agreement : —

" For example, let the effect a be crystallization. We compare
instances in which bodies are known to assume crystalline struc-
ture, but which have no other point of agreement ; and we find
them to have one, and as far as we can observe, only one,
antecedent in common : the deposition of a solid matter from a
liquid state, either a state of fusion or of solution. We conclude
therefore, that the solidification of a substance from a liquid state
is an invariable antecedent of its crystallization." ^

It is impossible here to detect any succession. A
substance does not first solidify, and then crystallize.
What has been discovered, if anything, is not a fact of
succession, but one of coexistence.

1 Logic, p. 279.

Mr. Mill's Four Experimental Methods. 109

But in what sense is solidification the cause of
crystallization ? It is not the material cause ; the
sugar, alum, or other substance is the material cause.
It is not the energetic cause ; that is some peculiar
kind of cohesion. It is not the historical cause ; for
the event solidification does not precede the event
crystallization. Solidification is not the " uncon-
ditional, invariable antecedent " of crystallization, for
many substances solidify without crystallizing. All
that the investigation has shown is, that if materials
take the forms of regular solids, they assume regularity
when they assume solidity. We have discovered not a
noun or a verb, but an adverb ; the time of solidifying
is the time of regularly solidifying.

Mr. Mill seems never to have considered whether, in
a sentence, "the cause" is the noun or the verb or
some other part of speech. If " Cain killed Abel," was
Cain the cause of Abel's death, or was the "killing"
the cause } Was it the arrival of Bliicher at Waterloo
that caused the defeat of Napoleon, or was it Bliicher
himself.'^

3. Mr. Mill's joint method of Agreement and Differ-
ence is wholly an illusion. There is no such method
known to science. The discovery of several instances
agreeing in nothing has no probative force whatever.
If twice after eating lobster I have been ill, the belief
that the lobster was the cause of the illness receives
no particle of support from the facts that a concave
lens disperses light, and that the Turks captured Con-
stantinople.

Dr. Fowler saw that Mr. Mill's statement was defec-
tive, and added the condition that the negative instances

no Inductive Logic,

must be "within the same department of investiga-
tion," that is, they must be good enough for use
according to the single method of difference. It is,
indeed, often possible to prove a fact independently,
both by the test of agreement and by the test of dif-
ference ; but the combination of these two independ-
ently sufficient proofs is not at all what Mr. Mill
means by his joint method. In the observations upon
the cause of dew, which Mr. Mill and Dr. Fowler use
as an illustration of the double rhethod, it was first
shown, by a primary induction, that all bodies upon
which dew is deposited agree either in losing heat
rapidly or in conducting it slowly, that is they have a
lower temperature than the air ; then the universal
negative was admitted, that dew is never found on any
other bodies ; and then it was inferred that the property
of being cooler than the surrounding air was the sole
cause of dew. It is obvious that this was something
very different from finding two instances of agreement
and two instances agreeing in nothing. Mr. Mill
says : —

"It thus appears that the instances in which much dew is
deposited, which are very various, agree in this, and, so far as we
are able to observe, in this only, that they either radiate heat
rapidly or conduct it slowly : qualities between which there is no
other circumstance of agreement than that by virtue of either, the
body tends to lose heat from the surface more rapidly than it can
be restored from within. The instances, on the contrary, in
which no dew, or but a small quantity of it, is formed, and which
are also extremely various, agree (as far as we can observe) in
nothing except in not having this same property. We seem,
therefore, to have detected the characteristic difference between
the substances on which dew is produced and those on which it is

Mr. Mill's Four Experimental Methods. iii

not produced. And thus have been reahzed the requisitions of
what we have termed the Indirect Method of Difference, or the
Joint Method of Agreement and Difference." ^

Here several things are confused. The pure method
of difference was employed in showing that bodies with
dew differed from those without dew simply in being
colder than the air. An exhaustive examination estab-
lished the general negative that dew occurs nowhere
else ; but this proves, not that coldness is the cause of
dew, but that there is no other cause. Suppose that
the question had been of heating caused by friction.
Two cases agreeing only in the circumstance friction,
and in the event heating, would meet the requirements
of the first part of the canon ; but we cannot prove
the universal negative that heating never occurs without
friction, and it is inconceivable that any confirmation
could be found in the properties of lenses, or the fall of
Constantinople.

Dr. Fowler added to Mr. Mill's canon the words :
" Moreover (supposing the requirements of the Method
to be rigorously fulfilled), the circumstance proved by
the method to be the cause is the only cause of the
phenomenon." He does not tell us how the require-
ment of finding "two or more instances from which
the phenomenon is absent " can be rigorously fulfilled,
but a little reflection will show that it is by proving a
universal negative ; this, certainly, is rigor in finding
"two or more " negative instances.

4. The Method of Concomitant Variations, which
corresponds to our Cases 3 and 4 under Canon i, is
used upon some very interesting facts, but logically

1 Logic, p. 299.

112 Inductive Logic.

has no distinctness from the ordinary method of differ-
ence. Nor does the language need to be so elastic.
The cases in which the consequent seems to decrease
when the antecedent increases are only verbally different
from those in which both increase together. All can be
stated in terms of increase. For instance, instead of
saying "the more heat the less condensation," we may
say "the more expansion." Each pair of instances of
concomitant variation affords a complete opportunity
for the regular application of the test of difference, and
the other pairs of cases, which are innumerable, simply
enable us to proceed at once to a primary induction.

5. Mr. Mill seems to have exaggerated, with paternal
partiality, the importance of these methods, which he
had formulated and named and presented to the philo-
sophical world. He says : —

"The four methods which it has now been attempted to
describe, are the only possible modes of experimental inquiry —
of direct induction a posteriori^ as distinguished from deduction;
at least I know not, nor am able to imagine any others. And
even of these, the Method of Residues, as we have seen, is not
independent of deduction ; though, as it also requires specific
experience, it may, without impropriety, be included among
methods of direct observation and experiment. These then, with
such assistance as can be obtained from deduction, compose the
available resources of the human mind for ascertaining the laws
of the succession of phenomena." 1

According to this, the whole of Induction is concerned
with facts of causation ; no place is reserved for facts
of coexistence or of likeness, or for the inductions
built upon them. Nor, indeed, is any explicit provision

1 Logic, p. 291.

Mr. Mill 'i- Four Experimental Methods. 113

made for constructing inductions of any kind out of
facts. But the facts isolated by these tests must be
treated by the mind just hke any other data of observa-
tion. They are not inductions, but must be generalized
into primary inductions, or syllogized into secondary or
mixed inductions, if they are to teach us anything.
The test of difference gives immediate certainty, each
time, regarding one solitary fact of causation. The test
of agreement gives, upon the comparison of the first
two instances, only a slight presumption of one fact of
causation, but this slight probability, upon the compar-
ison of more instances, gradually strengthens into a
primary induction of a causal connection in all the
instances. It should not be forgotten that no general
truth can ever be reached in inductive logic except by
a primary induction, directly used, or applied as one of
the premises of a syllogism. Mr. Mill seems to think
that all of the inductive thought of antiquity was
simple enumeration, and that the use of the methods is
the characteristic of modern science. He speaks of
" the ancients with their inductio per enumerationein
simplicem,'' somewhat contemptuously. But, of course,
the ancients isolated facts, by the methods of agreement
and of difference, every hour of their lives ; for they
could not make primary inductions without isolating
facts. The thinking of the ancients was inexact, but
they were not unaccustomed to any fundamental opera-
tion of the mind. The characteristic difference between
their thinking and ours cannot be, that we have sub-
stituted precision in isolating facts, for rashness in
generalizing ; the two things are not in the same
plane. It is impossible to avoid the belief that what

114 Inductive Logic.

led Mr. Mill to regard the methods as so much more
scientific than inductio per e^iumerationem simplicem
was the deductive process, involved in making a secon-
dary induction, which he immediately performed after
isolating a single fact of causation, and by which he
reached at once a trustworthy generalization.

CHAPTER XIII.

HYPOTHESIS.

Whenever we meet with a disconnected fact, the
mind instinctively seeks to refer it to some place
in the general order. An Hypothesis is a conjec-
ture made to account for some unexplained fact or
facts. To account for a fact is to refer it to some
uniformity or conjunction of uniformities. To speak
then more exactly, an Hypothesis is the reference of a
fact to a uniformity or a conjunction of uniformities,
before we have evidence enough to feel sure about it.
The word Theory is often used as synonymous with
hypothesis ; but it would be better to call the reference
an hypothesis before we feel sure of its truth, and a
theory after we become sure.

There is no other way to account for facts, except to
refer them to uniformities. For the uniformities them-
selves, no reason can be given. The mind is satisfied
with them as finalities. If one asks. Why is that bird
black } and is answered, That is a crow and all crows
are black, he accepts that answer as sufficient. Or if,
being a chemist, he is led to ask. What pigment makes
the crow's feathers black.? when he finds the presence
of a certain substance which is always black, he is
satisfied. Newton asks why that apple falls, and
having generalized that all things fall towards each
other, is glorified as having explained the fall of the
apple.

Ii6 Inductive Logic.

Writers upon inductive logic often please themselves
with the notion that they are looking deeper into
nature than its uniformities ; but this is a delusion.
Professor Minto says : —

"Science aims at reaching 'the causes of things': it tries to
penetrate behind observed uniformities to the explanation of them.
In fact, as long as a science consists only of observed uniformi-
ties, as long as it is in the empirical stage, it is a science only by
courtesy. Astronomy was in this stage before the discovery of
the Law of Gravitation. Medicine is merely empirical as long as
its practice rests upon such generalizations as that Quinine cures
ague, without knowing why. It is true that this explanation may
consist only in the discovery of a higher or a deeper uniformity,
a more recondite law of connection : the point is that these deeper
laws are not always open to observation, and that the method of
reaching them is not merely observing and recording." i

It would be much clearer to say simply that science
aims to discover the highest and deepest uniformities,
and is not satisfied until it has analyzed the so-called
■^empirical laws," that is, the uniformities which arise
from the co-operation of simpler ones, into their factors.
The " Laws of Nature " are merely the uniformities of
the resemblances, coexistences, and reactions of things.
No uniformity of any kind is open to observation in
the sense that it can be known by simply observing
and recording, without a mental process. The methods
of discovering the deeper uniformities differ in no way
from those used in discovering the empirical ones, nor
is there any line which marks the boundary between
the more and less complex uniformities.

Every person is constantly making hypotheses.
Every sensation that comes to the mind challenges an

1 Logic, p. 268.

Hypothesis. 117

explanation. It demands to be in some way classified,
and refuses to give us rest until disposed of. The
ordinary course is to refer the new phenomenon at
once to some known uniformity, but often most mis-
takenly. An amusing illustration occurs in the Life
and Letters of Charles Darwin : —

" When at Cambridge I used to practice throwing up my gun
to my shoulder before a looking-glass to see that I threw it up
straight. Another and better plan was to get a friend to wave
about a lighted candle, and then to fire at it with a cap on the
nipple, and if the aim was accurate the little puff of air would
blow out the candle. The explosion of the cap caused a sharp
crack, and I was told that the tutor of the college remarked,
"■ What an extraordinary thing it is, Mr. Darwin seems to spend
hours in cracking a horse-whip in his room, for I often hear the
crack when I pass under his window.' " ^

The tutor formed an hypothesis ; he referred the
sound which he heard to the uniformity which, among
those that he knew, it most resembled.

Since, in the production of any event, a large number
of uniformities frequently coincide, most hypotheses
are somewhat complex, but their essential nature is the
same.

No criterion can be fixed by which it may be decided
when the reference of a fact to a uniformity passes
from the condition of an hypothesis to that of an
induction. When the mind is satisfied that there is
proof enough, the hypothesis becomes an induction.
This point will be reached much more readily by some
minds than by others. Professor Huxley regarded the
opinion that modern horses are descended from small

1 Page 31.

Ii8 Inductive Logic.

five-toed progenitors as "demonstratively established,"
while many others still looked upon evolution as a very
slenderly supported hypothesis.
An Hypothesis is legitimate: —

1. When it includes all the known facts in the case.

2. When it is the simplest that has been suggested.

3. When the supposed phenomena fall into the lines
of known uniformities.

This third requirement is, we believe, what Sir
Isaac Newton meant by laying down the rule that the
hypothesis must assign a vera catcsa, a true cause. He
could not have meant that no new cause must be
assumed, for the very purpose of hypothesis is to deal
with new things. He could not have meant that the
cause assumed must be the r^<^/ cause; for that would
have been a foolish truism. He must have meant
that the assumed uniformity was to be of a kind
already known to exist. For example, if an explosion
occurs in a flouring mill, we may adopt the hypothesis
that it was caused by the fine, floating dust of flour, in
sudden combustion. Many substances have the prop-
erty of explosive combustion ; this is a vera causa. If
flour has this property, it but adds one more in an
already established line of uniformity. But should we
assume that the explosion was caused by ghosts, this
would not be in line with what is known to happen in
other cases ; we should have not only a new cause, but
a new kind of cause.

An hypothesis is illegitimate when it violates any
one of the foregoing rules. It is gratuitous when it
violates the second rule, or when there are no unex-
plained facts to start with. It is irrational to make a

Hypothesis. 119

gratuitous hypothesis, for inductive science cannot let
go of facts.

Mr. Mill's definition is as follows: —

" An hypothesis is any supposition which we make (either with-
out actual evidence, or upon evidence avowedly insufficient), in
order to endeavor to deduce from it conclusions in accordance
with facts which are known to be real ; under the idea that, if the
conclusions to which the hypothesis leads are known truths, the
hypothesis itself either must be, or at least is likely to be, true." ^

Mr. Mill lays it down as a condition of a genuinely
scientific hypothesis, "that it be not destined always
to remain an hypothesis, but be certain to be either
proved or disproved by that comparison with observed
facts which is termed verification." This condition we
cannot accept ; the mind is impelled to account for the
phenomena about it in the simplest and most harmo-
nious manner possible, and the question of expectation
for the future is wholly irrelevant. The hypothesis
that a certain ship that sailed away from port and
never was heard from again, ran into an iceberg, is
perfectly legitimate, if it accounts for all the facts, is
the simplest suggested, and is in line with what hap-
pens in that part of the ocean. Whether we expect
to find hereafter some of the wreckage, it is not neces-
sary to consider.

The right use of hypothesis was well illustrated in
the discovery of the planet Neptune. For some time
it had been observed, that the orbit of the planet
Uranus was subject to an amount of perturbation
which could not be accounted for from the influence of
known planets.

1 Logic, p. 349.

I20 Inductive Log-ic.

" Of the various hypotheses formed to account for it [the per-
turbation], during the progress of its development, none seemed
to have any degree of rational probability but that of the exist-
ence of an exterior, and hitherto undiscovered, planet, disturbing,
according to the received laws of planetary disturbance, the
motion of Uranus by its attraction, or rather superposing its dis-
turbance on those produced by Jupiter and Saturn, the other two
of the old planets which exercise any sensible disturbing action on
that planet. Accordingly, this was the explanation which natu-
rally, and almost of necessity, suggested itself to those conversant
with the planetary perturbations who considered the subject with
any degree of attention. The idea, however, of setting out from
the observed anomalous deviations, and employing them as data
to ascertain the distance and situation of the unknown body, or,
in other words, to resolve the inverse problem of perturbations,
'given the disturbances, to find the orbit and the place in that
orbit of the disturbing planet,' appears to have occurred only to
two mathematicians, Mr. Adams in England and M. Leverrier in
France, with sufficient distinctness and hopefulness of success to
induce them to attempt its solution. Both succeeded, and their
solutions, arrived at with perfect independence, and by each in
entire ignorance of the other's attempt, were found to agree in a
surprising manner when the nature and difiiculty of the problem
is considered ; the calculations of M. Leverrier assigning for the
heliocentric longitude of the disturbing planet for the 23rd Sept.,
1846, 326° o', and those of Mr. Adams (brought to the same date)
329° 19', differing only 3° 19'; the plane of its orbit deviating very
slightly, if at all, from that of the ecliptic.

"On the day above mentioned — a day forever memorable in
the annals of Astronomy — Dr. Galle, one of the astronomers
of the Royal Observatory at Berlin, received a letter from M.
Leverrier, announcing to him the result he had arrived at, and
requesting him to look for the disturbing planet in or near the
place assigned by his calculation. He did so, and on that very
night actually found it. A star of the eighth magnitude was seen
by him and by M. Encke in a situation where no star was marked
as existing in Dr. Bremiker's chart, then recently published by the
Berlin Academy. The next night it was found to have moved

Hypothesis. 121

from its place, and was therefore assuredly a planet. Subsequent
observations and calculations have fully demonstrated this planet,
to which the name of Neptune has been assigned, to be really
that body to whose disturbing attraction, according to the New-
tonian law of gravity, the observed anomalies in the motion of
Uranus were owing.^

The manner in which scientific men construct theo-
ries may be illustrated by Darwin's conjectures as to
the formation of coral islands : —

" Stibsidence Theory of Darwin. — This theory explains not
only atolls, but also barriers, and connects both in a satisfactory
manner with fringing reefs. It supposes that the sea-bottom,
where atolls and barriers occur, has been for ages subsiding, but
at a rate not greater than the upward building of the coral-ground ;
that every reef commences as a fringing reef, but, in the progress
of subsidence, was converted first into a barrier and finally into
an atoll. For, as the volcanic island went down, the corals would
build upward on the same spot ; and as the island would become
smaller and smaller, and the corals would grow faster on the outer
side of the reef, where they are exposed to the breakers, it is evi-
dent that the reef would become separated from the island by a
ship-channel, and thus become a barrier. Finally, when the island
disappears entirely, the reef, still building upward, would become
an atoll. ... It is seen that the corals do not build a vertical
wall, and therefore that the atoll is always smaller than the coast-
line of the original island. Consequently, if the subsidence
continues, a typical atoll is changed into a small, closed lagoon,
and, finally, into a lagoonless island. These, therefore, indicate
the deepest subsidence,

'■'•Evidences. — i. This theory accounts for all the more obvious
phenomena of atolls, such as their irregular circular form, their
size, the steepness of their outer slopes, etc. 2. Every stage of
gradation between the fringing reef on the one hand, and the atoll
on the other, has been traced by Dana, strongly suggesting that

1 Herschel's Outlines of Astronomy, fourth ed., §§ 767, 768, quoted
by Fowler, Inductive Logic, pp. 177, I'jZ.

122 Inductive Logic,

they are all different stages of development of the same thing.
We have in the Pacific some high islands, which are surrounded
by a pure fringing reef ; others in which the reef is a fringe on
one side and a barrier on the other ; others in which the barrier
is one mile, two miles, five miles, ten miles, twenty, or thirty miles
distant ; others which are called atolls, but the point of the
original volcanic island is still visible in the middle of the lagoon ;
others which are perfect atolls, but, by sounding, the head of the
drowned volcanic island is still detectable. The next .step in the
series is the perfect atoll, then the small atoll, and, finally, the
lagoonless coral island. These last kinds show that the original
island has gone down deeply. 3. By grappling-hooks ^<?^^ coral-
trees have been broken off and brought up from the ground
where they once grew, now far below the limiting depth of coral
growth. The evidence of subsidence in this case is of the same
kind and force as that derived from submerged forest-ground.
The corals have been carried below their depth and drowned. 4.
The remarkable distribution of the various kinds of reefs brought
to light by Dana is satisfactorily explained by this theory, and
therefore is an argument in its favor. In the middle of the atoll
region of the Pacific there is a blank area^ 2000 miles long and
1000 or more miles wide, where there are no islands. Next
about this is an area in which small atolls predominate ; about
this again the region of ordinary atolls ; beyond this the region
mostly of barriers, and finally of fringes. Now, by this theory
this distribution is thus explained : The sea-bottom in the blank
area has gone down so fast that the corals have not been able to
keep pace, and have therefore been drowned, and left no monu-
ment of their existence. In the next region the corals have been
able to keep within living distance of the surface, but the original
islands have not only disappeared, but gone down to great depths.
In the next the original high islands have disappeared, but not
gone down so deep ; in the next they have sunk only to the mid-
dle. The fringing reefs stand on the margin of the sinking area.
Outside of this again there is in some places even evidence of
upheaval instead of subsidence. Raised beaches in the form of
fringing-reef rocks are found clinging to the sides of high islands
many feet above the present searlevel. 5. In some places this

Hypothesis. 123

subsidence seems to be still in progress. On certain coral islands
sacred structures of stone made by the natives are now standing
in water, and the paths worn by the feet of devotees are now
passages for canoes (Dana)."

^^ Murray's Theory. — Recently serious doubts have been cast
on Darwin's subsidence theory, at least as a universal explanation
of barriers and atolls. Mr. Murray, from his observations during
the voyage of the Challenger^ believes that barriers and atolls may
be explained without subsidence of the sea-floor. An outline of
his views may be thus stated: (i) Submarine banks formed in
any way, either {a) built up by accumulating shells of successive
generations of marine animals, until within the reach of coral
growth ; or {b^ by volcanic cinder cones cut down by the waves
so as to form suitable banks. (2) The banks taken possession of
by corals are built up to the sea-level. (3) The coral growth is
confined, or at least most rapid, on the outer margin, because
exposed to the action of the sea. Thus arises a ring with blank
space within. (4) The action of waves beats these rings into a
series of islets. (5) Meanwhile the scouring action of currents
and the solvent action of sea-water scoops out the blank area into
a more or less deep lagoon. (6) The action of waves breaking
the living coral and the reef-rock forms a debris-^^^ or talus, with
steep outward slope, on which the corals continue to grow sea-
ward into deep water. Thus the coral ring continues to spread,
like 2. fairy ring, by growing seaward in every direction, and dying
behind. (7) According to Darwin, atolls grow continually smaller;
according to Murray, they grow continually larger.

" Barriers are similarly explained. They commence as fringes,
which grow seaward as far as depth will allow. Then the corals
die near the shore, and this part is scoured out into a channel.
Meanwhile the reef extends seaward on its own talus, and the
channel is pari passu widened.

" In the present condition of the question it is probable that
there are more ways than one in which barriers and atolls may be
formed, but Darwin's view seems still to hold its own as a general,
though not as a universal theory." ^

1 Le Conte's Geology, pp. 150-153.

124 Inductive Logic.

The formation of wise hypotheses is the most impor-
tant step in the progress of science. It is simply
suspecting the lines of nature's uniformity from slight
hints. The fundamental preparation for it is intimate
familiarity with the general system of things, so far as
discovered. Helmholtz has well stated the case in the
following passages. It will be observed that instead
of "foreknowledge" it would have been better to use a
more general word. Induction has as much to do with
the past, the distant, and the unobservable present, as
it has to do with the future. It deals with all of these
not as past, present, and future, but as unseen parts of
the existing order ; it is able to reason about them only
as parts of that order.

" In order to acquire this foreknowledge of what is coming, but
of what has not been settled by observations, no other method is
possible than that of endeavoring to arrive at the laws of facts by
observations ; and we can only learn them by induction, by the
careful selection, collation, and observation of those cases which
fall under the law. When we fancy that we have arrived at a law,
the business of deduction commences. It is then our duty to
develop the consequences of our law as completely as may be, but
in the first place only to apply to them the test of experience, so
far as they can be tested, and then decide by this test whether the
law holds, and to what extent. This is a test which really never
ceases. The true natural philosopher reflects at each new phe-
nomenon, whether the best established laws of the best known
forces may not experience a change ; it can, of course, only be a
question of a change which does not contradict the whole store of
our previously collected experiences. It never thus attains uncon-
ditional truth, but such a high degree of probability that it is
practically equal to certainty." ^

"In speaking against the empty manufacture of hypotheses, do
not by any means suppose that I wish to diminish the real value

1 Helmholtz, Populat' Scientific Lectures^ p. 226.

Hypothesis. 125

of original thoughts. The first discovery of a new law, is the
discovery of a similarity which has hitherto been concealed in the
course of natural processes. It is a manifestation of that which
our forefathers in a serious sense described as 'wit'; it is of the
same quality as the highest performances of artistic perception in
the discovery of new types of expression. It is something which
cannot be forced, and which cannot be acquired by any known
method." 1

Dr. Whewell has discussed at length the cause of the
failure of the Greek physical philosophy. From this
discussion we will make a few extracts : —

" The cause of the failure of so many attempts of the Greeks
to construct physical science is so important, that we must endeavor
to bring it into view here ; though the full development of such
subjects belongs rather to the Philosophy of Induction.

" The cause of failure was not the Jteglect of facts. It is often
said that the Greeks disregarded experience, and spun their philoso-
phy out of their own thoughts alone ; and this is supposed by
many to be their essential error. It is, no doubt, true that the
disregard of experience is a phrase which may be so interpreted
as to express almost any defect of philosophical method ; since
coincidence with experience is requisite to the truth of all theory.
But if we fix a more precise sense on our terms, I conceive it may
be shown that the Greek philosophy did, in its opinions, recognize
the necessity and paramount value of observations ; did, in its
origin, proceed upon observed facts, and did employ itself to no
small extent in classifying and arranging phenomena.

" ' The way must be the same,' says Aristotle, in speaking of
the rules of reasoning, ' with respect to philosophy, as it is with
respect to any art or science whatever ; we must collect the facts
and the things to which the facts happen, in each subject, and
provide as large a supply of these as possible.'

" We come back, again, therefore, to the question, What was
the radical and fatal defect in the physical speculations of the
Greek philosophical schools ?

1 Helmholtz, Popular Scientific Lectures, p. 227.

126 Inductive Logic.

" To this I answer : The defect was, that though they had in
their possession Facts and Ideas, the Ideas were not distinct
and appropriate to the facts.

" The peculiar characteristics of scientific ideas, which I have
endeavored to express by speaking of them as distinct and
appropriate to the facts, must be more fully and formally set forth
when we come to the philosophy of the subject. In the meantime,
the reader will probably have no difficulty in conceiving that for
each class of Facts there is some special set of Ideas, by means of
which the facts can be included in general scientific truths ; and
that these Ideas which may thus be termed appropriate., must be
possessed with entire distinctness and clearness, in order that they
may be successfully applied. It was the want of Ideas having this
reference to material phenomena which rendered the ancient phi-
losophers, with very few exceptions, helpless and unsuccessful
speculators on physical subjects." ^

The point which Dr. Whewell makes here seems to
us exactly provided for in the third rule given above
for legitimate hypotheses. The Greeks failed, because
their conjectures were not in the lines of known uni-
formities of nature. They sought the causes of
phenomena in abstract and general conceptions.

Important as is the function of hypotheses, it may
yet be exaggerated. Thus, Professor Davis, says: —

" It is equally obvious that all experimental observation is like-
wise dependent on supposition. A mere trial of possible combina-
tions to see what will come of them, without the further sugges-
tions of a suggested supposition, can elicit nothing, save by
chance." ^

But it is plain that a chemist may take the contents of
the stomach of a murdered man, and may test succes-
sively for arsenic, strychnine, and other poisons, with-

1 Whewell's History of the Inductive Sciences, vol. i, pp. Z^^, 87.

2 Inductive Logic, p. 1 59.

Hypothesis. 127

out any hypothesis whatever ; and that he will reach
the truth just as quickly without an hypothesis as with
one. In every chemical laboratory, students are taught
a regular system of tests, by which any questionable
substance may be quickly identified without an hypoth-
esis. Indeed, the tendency of science is to dispense
with hypotheses as guides in research, to cease asking
nature "leading questions," and to carry investigations
forward on plans that permit the facts to speak for
themselves. It is a waste of time to frame an hypoth-
esis before all of the facts which can be ascertained
are in hand.

Dr. Fowler says: —

" Even though a hypothesis may ultimately be discovered to be
false, it may be of great service in pointing the way to a truer
theory. Thus, as already remarked, the circular theory of plane-
tary motion, and the supplementary theory of epicycles and eccen-
trics, undoubtedly contributed to the formation of the hypothesis
which was eventually proved true. Kepler himself tried no less
than nineteen different hypotheses before he hit upon the right
one, and his ultimate success was, doubtless, in no slight degree
due to his unsuccessful efforts. There is hardly any branch of
science in which it might not be affirmed that without a number of
false guesses true theories could never have been attained." ^

The service which a false hypothesis renders is rather
moral then intellectual. The belief that one has found
a clue to the truth tends to keep up courage, and
courage is necessary to persistent work upon the facts.
But the false hypothesis, in itself considered, is purely
a disadvantage and waste of time ; it is, like every false
scent, a diversion from the right path. In searching

^ Inductive Logic, p. 99.

128 Inductive Logic.

for something, we are not likely to strike upon it at the
first effort ; and therefore our false guesses may be
said to be necessary to our success. Where there are
a number of equal possibilities, one must begin some-
where, and go on proving negatives, until the right one
is reached. If a paper is in the desk, and there are
four drawers, one as likely to contain it as another, the
successive hypotheses that it is in the first, second, and
third, will keep us looking, and when they are exploded
we shall know that it is in the fourth. There is no abso-
lute way to escape the tedium of testing wrong hypoth-
eses, but we are fortunate in proportion to the fewness
of those that we make, and the best rule is to delay in
making any conjecture as long as possible. Grant's
disastrous charge at Cold Harbor was necessary to his
final victory over Lee, simply in showing that if he was
ever to conquer, it must be in some other way ; this is
all of the intellectual value that can ever attach to a
false hypothesis.

CHAPTER XIV.
INDUCTIVE ARGUMENTS.

Having considered the elementary steps of inductive
investigation, we now advance to the construction of
inductive arguments.

A very common form of argument is that from
Analogy. Such an argument is based upon a primary
induction of a uniformity of resemblances. Having
observed a certain object to have, in many respects,
the property x, we come to think that we are upon the
line of one of its uniformities, and that it will be found
to have, in all respects, the property x. But ;r may
stand for resemblance to some other object.

As Bishop Butler has said: —

"Probable evidence is essentially distinguished from demonstra-
tive by this, that it admits of degrees, and of all variety of them,
from the highest moral certainty to the very lov/est presumption.
We cannot, indeed, say a thing is probably true upon one very
slight presumption for it ; because, as there may be probabihties
on both sides of the question, there may be some against it ; and
though there be not, yet a slight presumption does not beget that
degree of conviction which is implied in saying that a thing is
probably true. But that the slightest possible presumption is of
the nature of a probability, appears from hence, that such low-
presumption, often repeated, will amount even to moral certainty.
Thus, a man's having observed the ebb and flow of the tide to-day,
affords some sort of presumption, though the lowest imaginable,
that it may happen again to-morrow ; but the observation of this
event for so many days and months, and ages together, as it has
been observed by mankind, gives us a full assurance that it will." ^

1 Introduction to the Analogy of Religion.

130 Inductive Logic.

Now a uniformity of resemblances is just like any
other line of uniformity, and the argument from it is
the same. If I have often found a substance white, I
begin to expect to find it of that color next time ; and if
I have found it to resemble another substance in many
respects, I expect to find more resemblances. An
argument from Analogy, therefore, does not differ in
any way from an argument based upon any other
primary induction. A primary induction may be made
that the peach trees of a certain region yield a crop
three seasons out of four ; and this becomes the basis
of expectation. Just so the induction may be made
that two objects resemble each other in three respects
out of four (or according to any other ratio), and this
will measure the probability of resemblance in any
unexamined instance.

The following example of the use of the argument
from analogy is taken from the Scientific Papers of
Asa Gray : —

" The most interesting ideas connected with trees are those
suggested by their stability and duration. They far outlast all
other living things, and form the familiar and appropriate symbols
of long-protracted existence. ^ As tlie days of a tree shall be the
days of my people ' is one of the most beautiful and striking figures
under which a blessing can be conveyed. We are naturally led
to inquire, whether there is any absolute limit to their existence.
If not destroyed by accident, — that is, by extrinsic causes, of
whatever sort, — do trees eventually perish, like ourselves, from
old age? It is commonly thought, no doubt, that trees are fully
exposed to the inevitable fate of all other living things. The
opposite opinion seems to involve a paradox, and to be contra-
dicted by every one's observation. But popular opinion is an
unsafe guide ; — the more so in this case, as our ordinary concep-
tions on the subject spring from a false analogy, which we have

Inductive Arguments. 131

unconsciously established, between plants and animals. This
common analogy might, perhaps, hold good, if the tree were actu-
ally formed like the animal, all the parts of which are created at
once in their rudimentary state, and soon attain their fullest devel-
opment, so that the functions are carried on throughout life in the
same set of organs. If this were the case with the tree, it would
hkewise die, sooner or later, of old age, — would perish from
causes strictly analogous to those which fix a natural limit to the
life of animals. The unavoidable induration and incrustation of
its cells and vessels, apart from other causes, would put an early
and sure Hmit to the life of the tree, just as it does in fact terminate
the existence of the leaf, the proper emblem of mortality, — which,
although it generally lives only a single season, may yet truly be
said to die of old age. But, as the leaves are necessarily renewed
every year, so also are the other essential organs of the plant.
The tree is gradually developed by the successive addition of new
parts. It annually renews not only its buds and leaves, but its
wood and its roots ; everything, indeed, that is concerned in its
life and growth. Thus, like the fabled ^son, being restored from
the decrepitude of age to the bloom of early youth, — the most
recent branchlets being placed, by means of the latest layer of
wood, in favorable communication with the newly-formed roots,
and these extending at a corresponding rate into fresh soil, —

' Quae quantum vertice ad auras
^therias, tantum radice in Tartara tendit,'

why has not the tree all the conditions of existence in the thou-
sandth that it possessed in the hundredth, or the tenth, year of its
age ? The old and central part of the trunk may, indeed, decay ;
but this is of little moment, so long as new layers are regularly
formed at the circumference. The tree survives, and it is difficult
to show that it is liable to death from old age in any proper sense
of the term. Nor do we arrive at a different conclusion when we
contemplate the tree under a less familiar but more philosophical
aspect, — considering it not as a simple individual, like man or the
higher animals, but as an aggregate of many individuals, which,
though ordinarily connected with the parent stalk, are capable of

132 Inductive Logic.

growing by themselves, and, indeed, often do separate spontane-
ously, and in a variety of ways acquire independent existence. If,
then, the tree be, as it undeniably is, a complex being, an aggre-
gate of as many individuals, united in a common trunk, as there
are, or have been, buds developed on its surface ; and if the com-
ponent individuals be annually renewed, why should not the
aggregate, the tree^ last indefinitely? To establish a proper anal-
ogy, we must not compare the tree with man, but with the coral
formations, in which numberless individuals, engrafted and blended
on a common base, though capable of living when detached from
the mass, conspire to build up those arborescent structures so
puzzling to the older naturalists that they were not inappropriately
named ^ zoophytes,' or animal-plants. The immense coral-groves,
which have thus grown up in tropical seas, have, no doubt, endured
for ages ; the inner and older parts consisting of the untenanted
cells of individuals that have long since perished, while fresh
structures are continually produced on the surface. The individ-
uals, indeed, perish, but the aggregate may endure as long as time
itself. So with the tree, considered under this point of view.
Though the wood in the center of the trunk and large branches —
the produce of buds and leaves that have long ago disappeared
— may die and decay, yet while new individuals are formed upon
the surface with each successive crop of fresh buds, and placed in
as favorable communication with the soil and the air as their pre-
decessors, the aggregate tree would appear to have no necessary,
no inherent limit to its existence." ^

The question here is, whether the analogy, the uni-
formity of resemblance, is between the tree and an
individual animal, or between the tree and a community
of animals. Most readers will suspect that neither
analogy is complete enough to justify the conclusions
suggested.

The relation of primary and secondary inductions in
constructing an argument is admirably illustrated in

1 Vol. ii, p. 79.

Inductive Arguments. 133

the famous incident of Robinson Crusoe's discovery of
the solitary footprint in the sand. The story runs as
follows: —

" It happened one day, about noon, going towards my boat, I
was exceedingly surprised with the print of a man's naked foot on
the shore, whicli was very plain to be seen on the sand. I stood
like one thunderstruck, or as if I had seen an apparition. I listened,
I looked around me, but I could hear nothing nor see anything ; I
went up to a rising ground to look farther ; I went up the shore
and down the shore, but it was all one ; I could see no other
impression but that one."

Crusoe was already in possession of the primary
induction, " Impressions of a given form are made only
by men." Observation supplied the minor premise,
" Here is an impression of the given form." The
secondarily inductive conclusion followed, " A man
made this."

A more complex illustration may be taken from the
writings of the eminent glacialist, Professor G. Frederick
Wright : —

"In the summer of 1882, after having the previous year
completed, with Professor Lewis, the exploration of the glacial
boundary through Pennsylvania, I continued to work through the
state of Ohio, and traced the line at length to the Ohio River,
near Ripley, about sixty miles above Cincinnati. From this point,
for about thirty miles down the river, to the vicinity of New Rich-
mond, the glacial boundary lies upon the north bank of its trough;
till, bowlders, and scratched stones being found on the highlands
down to the extreme margin on the north side, but being absent
from the corresponding highlands on the Kentucky side. Near
Point Pleasant, the birth-place of President Grant, the river
makes a long bend to the north, continuing in this direction to
Cincinnati, and thence westward to North Bend, the home and
burial-place of President William Henry Harrison ; here it turns

134 Inductive Logic.

south again, thus forming in Kentucky a peninsula, as it were,
pointing to the north, and including the territory of Campbell,
Kenton, and Boone counties. Upon examining this district it
was found that in places in Campbell county, and over the whole
northern and western parts of Boone county, there were true
glacial deposits on the highest lands — the elevation near Burling-
ton being five hundred and fifty feet above low-water mark at
Cincinnati. In places, large numbers of bowlders of northern
origin were found stranded on the very summit-level of the region
— 2.<?., on the divide, between the short streams running north and
those running south, and between the Licking and the Ohio River.
They were also found south of this secondary divide, seven miles
back from the river, and five hundred feet above it (near Florence,
Boone county). Several were recognized as belonging to a species
of red jasper conglomerate, whose outcropping is well marked on
the northern shore of Lake Huron and above the outlet of Lake
Superior. These bowlders are very beautiful ; and, farther north,
where they are more abundant in the fields, are frequently used to
adorn the front-yards of residences or even for the construction of
public buildings. Some of the citizens of Cleveland, Ohio, have
brought large fragments for this purpose from the parent ledges.
But here, beside a roadway through the Kentucky hills, were large
specimens of this same conglomerate (one bowlder being nearly
three feet in diameter), which had been transported by glacial ice
fully six hundred miles from their native bed, and left to tell the
story not only of their own travels, but of other most interesting
events connected with the cause which transported them. These
glacial deposits south of the Ohio are such as to make it certain
that the front of the continental glacier itself pushed, at some
points, seven or eight miles beyond the Ohio River ; and it is
altogether probable that for a distance of fifty miles (or completely
around the eastern, northern, and western sides of the Kentucky
peninsula formed by the great bend of the river), the ice came
down to the trough of the Ohio, and crossed it so as completely
to choke the channel, and form a glacial dam high enough to
raise the level of the water five hundred and fifty feet — this being
the height of the water-shed to the south. The consequences
following are interesting to trace.

Inductive Arguments, 135

" The bottom of the Ohio River at Cincinnati is 447 feet above
the sea-level. A dam of 553 feet would raise the water in its rear
to a height of 1000 feet above the tide. This would produce a
long, narrow lake, of the width of the eroded trough of the Ohio,
submerge the site of Pittsburg to a depth of 300 feet, and make
slack water up the Monongahela nearly to Grafton, W. Va., and
up the Alleghany as far as Oil City. All the tributaries of the
Ohio would Ukewise be filled to this level with the back water.
The length of this slack-water lake in the main valley, to its
termination up either the Alleghany or the Monongahela, was not
far from one thousand miles. The conditions were also peculiar
in this, that all the northern tributaries head within the southern
margin of the ice-front, which lay at varying distances to the north.
Down these northern tributaries there must have poured during
the summer months immense torrents of water to strand bowlder-
laden icebergs on the summits of such high hills as were lower
than the level of the dam." ^

Let US trace the inductive steps by which the
conclusion is reached that there was once a lake in
the valley of the Ohio. First there is the primary
induction that, "This red jasper conglomerate is
original only in Canada." This is proved only by an
exhaustive examination in detail of all the rocks i7t situ
in the whole region concerned, such examination being
continued until the mind of the investigator is satisfied
— a point not precisely definable. Next comes the
primary induction, "Angular and scratched bowlders
like these are the work of glaciers." This is a primary
induction made by the test of agreement by observation
upon living glaciers. The united observation of geolo-
gists over the whole world warrants another primary
induction, the universal negative, " No agents but
glaciers are making scratched bowlders." Observation

1 Ice Age in No7'th America., p. 326.

136 Inductive Logic.

gives us the fact, "There are angular and scratched
pieces of this jasper conglomerate in Boone county,
Kentucky." Next is the secondary induction, " The
ice-sheet extended into Boone county." But the
mathematical proposition may be affirmed, " An ice-
sheet extending from Canada into Boone county would
dam the Ohio River." Thus we reach at last the mixed
induction, " The Ohio River was once closed by an
ice-dam." Again it may be affirmed, " If there was a
dam, there was a lake"; which leads to the mixed
induction, " There was a lake." The validity of these
conclusions depends wholly upon the accuracy of the
observations, and the exhaustiveness of the exarriina-
tions by which the universal negatives are established.
The subject of Verification has been so luminously
presented by Dr. Fowler that nothing more will be
necessary than to quote his remarks : —

" In Deductive Reasoning, especially when it involves elaborate
calculations, there is always great danger lest we should have
omitted to take into account some particular agency or element,
or have miscalculated its effects, or have formed a false estimate
of the combined effect of the various agencies or elements in
operation. The only remedy against these possible errors, besides
the employment of great caution in the conduct of the deductive
process itself, is to be found in Verification, a word which, in its
stricter sense, appears to be applied to the process of testing, by
means of an appeal to facts, the validity of the conclusions already
arrived at by a course of deductive reasoning. Thus it had been
deductively inferred from the Copernican theory that the planets
Venus and Mercury ought to pass through phases, like the moon,
and the application of the telescope, by means of which they were
actually seen to assume these phases, furnished a triumphant
verification of the inference. Every occurrence of an eclipse of
the sun or moon or of the transit or occultation of a star, when it

Inductive Arguments. 137

accords with the previous calculations of astronomers, is also an
instance of Verification in this the stricter sense of the term. The
discovery of the planet Neptune affords an excellent instance of
the same kind. But the word is often used in a looser sense and
extended to all cases in which an appeal is made to facts, as, for
instance, when we perform an experiment in order to test the truth
of a hypothesis, or where we employ the Method of Difference in
order to supplement the characteristic uncertainty attaching to the
employment of the Method of Agreement. Of the process denoted
by this looser sense of the word, instances will readily occur to
every one. Thus, the diminution in the periods of Encke's comet
has been regarded by some astronomers (though, perhaps, errone-
ously) as a verification of the theory that space is filled with an
interstellar medium ; or, to take an instance from a very different
class of subjects, the recent breaking up of the slave system in the
Southern States of America may be regarded as a verification of
the prediction that slave and free institutions could not long
coexist under the same political form of government. For an
instance of a case in which the Method of Difference is called in
to verify a previous employment of the Method of Agreement, I
may refer back to the inquiry into the cause of crystallization,
already adduced in my discussion of those two methods.

" There is a still wider appHcation of the word Verification, by
which it is extended to any corroboration of one mode of proof by
means of another. It thus includes a deductive proof adduced in
corroboration of an inductive one. The most common instance of
this kind of verification is the inclusion of a partial under a more
general law, the partial law having been arrived at inductively,
and it being subsequently shown that the more general law leads
deductively to it. Thus, the phenomena of the Tides had, prior
to the epoch of Newton, been partially explained by the inductive
method. Newton, by deducing these phenomena from the Law
of Universal Gravitation, not only afforded a much more complete
explanation, but also furnished the most convincing verification of
the results already arrived at. Similarly the laws of falling bodies
on the earth's surface, which had already been proved inductively,
were, from the time of Newton, brought under the law of universal
gravitation, and proved deductively from it. The same was also

138 Indtictive Logic.

the case with Kepler's Laws, when they were proved deductively
from the theorem of the central force. This mode of verification
is recommended by Mr. Mill, under the name of the Inverse
Deductive or Historical Method, as specially appHcable to
generalizations on society which have been inferred inductively
from the study of history or the observation of mankind. These
generalizations are subsequently verified by being connected
deductively with the general laws of mind or conduct which are
furnished by the study of Psychology or Ethology. It is thus
shown that the generalizations of history are such as we might
have anticipated a priori from a general knowledge of human
nature, and each branch of the inquiry is made in this manner to
afford a striking confirmation of the results arrived at by the other.
"It need hardly be remarked that any verification of one
inductive proof by another, or of a deduction by an induction,
should conform with the laws of deductive or inductive reasoning
as the case may be. Verification is not a distinct mode of proof,
but is simply the confirmation of one proof by another, sometimes
of a deduction by an induction, sometimes of an induction by a
deduction, and, finally, sometimes of one induction or deduction
by another. It must also be borne in mind that the term is not
infrequently employed to designate simply the confirmation of a
hypothesis by an appeal to facts." ^

In trials at law the State sets itself to ascertain the
truth regarding certain alleged facts. The inquiry is a
strictly inductive one, and every part of the procedure
must, if just, illustrate the sound principles of this
branch of logic. Since the community cannot act
directly, special officers are appointed to represent it.
Everything is done by exact rules, which, although
they seem to the thoughtless to be arbitrary, have
been established because experience has shown that, by
the observance of them, truth will be, in the largest
number of cases, arrived at.

1 Inductive Logic, pp. 249-253.

hiductive Arguments. 139

Any criminal charge against a man is in the first place
submitted to a Grand Jury. This body passes upon the
question whether the hypothesis that the accused com-
mitted the offense charged is legitimate. It considers
whether there are any facts otherwise unexplained,
whether the proposed explanation will include all the
facts known, and whether the supposition of the crime
is the simplest explanation of the facts known of the
accused. If the answer to each of these inquiries is
affirmative, the Grand Jury reports " a true bill," or
legitimate hypothesis.

The case being brought to trial, since all inductive
proof proceeds from observation, witnesses are brought
to testify to their own observations.

"Oral evidence must in all cases be direct ; that is to say —

" If it refers to a fact alleged to have been seen, it must be the
evidence of a witness who says he saw it ;

" If it refers to a fact alleged to have been heard, it must be the
evidence of a witness who says he heard it ;

" If it refers to a fact alleged to have been perceived by any
other sense or in any other manner, it must be the evidence of a
witness who says he perceived it by that sense or in that manner;

" If it refers to an opinion or the grounds on which that opinion
is held, it must be the evidence of the person who holds that
opinion on those grounds." ^

The grounds upon which testimony is accepted have
been well set forth by David Hume in his famous essay
"Of Miracles":—

"All effects follow not with like certainty from their supposed
causes. Some events are found, in all countries and all ages, to
have been constantly joined together : others are found to have
been more variable, and sometimes to disappoint our expectations ;

1 Stephen's Digest of the Law of Evidence (Amer. ed.), p. 126.

140 Inductive Logic.

so that in our reasonings concerning matters of fact, there are all
imaginable degrees of assurance, from the highest certainty to the
lowest species of moral evidence.

" A wise man, therefore, proportions his belief to the evidence.
In such conclusions as are founded on an infallible experience, he
expects the event with the last degree of assurance, and regards
his past experience as ixiSS. proof oi the future existence of that
event. In other cases he proceeds with more caution : he weighs
the opposite experiments : he considers which side is supported
by the greater number of experiments : to that side he inclines
with doubt and hesitation ; and when at last he fixes his judgment,
the evidence exceeds not what we properly call probability. All
probability then supposes an opposition of experiments and obser-
vations, where the one side is found to overbalance the other, and
to produce a degree of evidence proportioned to the superiority.
A hundred instances or experiments on one side, and fifty on
another, afford a doubtful expectation of any event ; though a
hundred uniform experiments, with only one that is contradictory,
reasonably beget a pretty strong degree of assurance. In all
cases we must balance the opposite experiments, where they are
opposite, and deduct the smaller number from the greater, in
order to know the exact force of the superior evidence.

'^ To apply these principles to a particular instance ; we may
observe, that there is no species of reasoning more common, more
useful, and even necessary to human life, than that which is
derived from the testimony of men, and the reports of eye-witnesses
and spectators. This species of reasoning, perhaps, one may
deny to be founded on the relation of cause and effect. I shall
not dispute about a word. It will be sufficient to observe, that
our assurance in any argument of this kind is derived from no
other principle than our observation of the veracity of human
testimony, and of the usual conformity of facts to the report of
witnesses. It being a general maxim that no objects have any
discoverable connection together, and that all the inferences which
we can draw from one to another, are founded merely on our
experience of their constant and regular conjunction, it is evident
that we ought not to make an exception to this maxim in favor of
human testimony, whose connection with any event seems, in

Inductive Arguments. 141

itself, as little necessary as any other. Were not the memory
tenacious to a certain degree ; had not men commonly an inclina-
tion to truth and a principle of probity ; were they not sensible to
shame when detected in a falsehood : were not these, I say,
discovered by experience to be qualities inherent in human nature,
we should never repose the least confidence in human testimony.
A man delirious, or noted for falsehood and villany, has no
manner of authority with us.

" And as the evidence derived from witnesses and human
testimony is founded on past experience, so it varies with the
experience, and is regarded as 3. proof or 2i probability^ according
as the conjunction between any particular kind of report, and any
kind of object, has been found to be constant or variable.

" The reason why we place any credit in witnesses and histo-
rians, is not derived from any connection which we perceive a priori
between testimony and reality, but because we are accustomed to
find a conformity between them. But when the fact attested is
such a one as has seldom fallen under our observation, here is a
contest of two opposite experiences, of which the one destroys the
other as far as its force goes, and the superior can only operate
on the mind by the force which remains.

" / should not believe stich a story were it told 7Jte by Cato,
was a proverbial saying in Rome, even during the lifetime of that
philosophical patriot. The incredibility of a fact, it was allowed,
might invalidate so great an authority."

It is clear, then, that the reason why testimony is
received is that we have made the primary induction
that the testimony of respectable men is usually con-
joined with fact. It makes little difference whether
this conjunction be regarded as a fact of coexistence
or of causation.

When a man is charged with a crime, witnesses may
testify directly that they perceived him commit it.
Here the logical process is brief : Human testimony is
true ; These witnesses testify that they saw the act of

142 Inductive Logic,

crime ; Therefore the man is guilty. This is a secon-
dary induction.

But more often we must proceed by a longer road.
The witnesses cannot testify directly to the fact
charged ; they can testify only to other facts which
are related to the fact charged. Such facts are said to
be relevant to the fact in issue. The rules of Relevancy
are simply the statements of the primary inductions
which lawmakers have accepted as well established,
regarding the connections of certain kinds of facts.
Human testimony may be accepted as true ; but if
testimony is offered to a fact, the previous question
must be raised whether we have any primary induction
that the existence of the fact it is proposed to prove is
usually connected with the existence or non-existence
of the fact charged. In the famous Salem witchcraft
cases, which left so dark a blot upon the early history
of New England, the fallacy was that the relevancy of
the facts proved to the crime charged had not been
established by any induction. If the rulings of courts
appear to exclude certain kinds of evidence, commonly
accepted by private persons, it is because the primary
induction has been made that the connection of those
facts is uncertain, and because many persons are
extremely careless in adopting unsubstantiated reports.
There is nothing peculiar in the logic of courts, nor
should a single principle be admitted, except such as
judicious men apply in reaching their own private
conclusions.

The following statements of the principles of rele-
vancy are taken from Stephen's Digest of the Law of
Evidence : —

Inductive Arguments. 1 43

" Evidence may be given, in any proceeding, of any fact in issue,
and of any fact relevant to any fact in issue unless it is
hereinafter declared to be deemed irrelevant,

and of any fact hereinafter declared to be deemed relevant
to the issue whether it is or is not relevant thereto." ^

" Facts whether in issue or not, are relevant to each other
when one is, or probably may be, or may have been —
the cause of the other ;
the effect of the other ;
an effect of the same cause ;
a cause of the same effect :
or when the one shows that the other must or cannot have
occurred, or probably does or did exist or not ;

or that any fact does or did exist or not which in the common
course of events would either have caused or been caused by the
other ;

provided that such facts do not fall within the exclusive rules
contained in chapters iii, iv, v, vi ; or that they do fall within the
exceptions to those rules contained in those chapters." ^

Illustrations.

" (a) A's death is caused by his taking poison. The adminis-
tration of the poison is relevant to A's death as its cause. A's
death is relevant to the poisoning as its effect.

"(<^) A and B each eat from the same dish and each exhibit
symptoms of the same poison. A's symptoms and B's symptoms
are relevant to each other as effects of the same cause.

" {c) The question is, whether A died of the effects of a railway
accident.

" Facts tending to show that his death was caused by inflam-
mation of the membranes of the brain, which probably might be
caused by the accident ; and facts tending to show that his death
was caused by typhoid fever, which have nothing to do with the
accident, are relevant to each other as possible causes of tne
same effect — A's death.

1 Stephen's Digest^ p. 5.

2 Ibid., p. 246.

144 Inductive Logic.

" (^) A is charged with committing a crime in London on a
given day. The fact that on that day he was at Calcutta is rele-
vant as proving that he could not have committed the crime.

"(^) The question is, whether A committed a crime.

" The circumstances are such that it must have been committed
either by A, B, or C. Every fact which shows this, and every
fact which shows that neither B nor C committed it, or that either
of them did or*might have committed it, is relevant.

" (/") B, a person in possession of a large sum of money, is
murdered and robbed. The question is, whether A murdered
him. The fact that after the murder A was or was not possessed
of a sum of money unaccounted for is relevant, as showing the
existence or absence of a fact which, in the common course of
events, would be caused by A's committing the murder. A's
knowledge that B was in possession of the money would be
relevant as a fact, which, in the ordinary course of events, might
cause or be one of the causes of the murder.

" C^) -^ is murdered in his own house at night. The absence
of marks of violence to the house is relevant to the question,
whether the murder was committed by a servant, because it
shows the absence of an effect which would have been caused by
its being committed by a stranger." ^

" Four classes of facts, which in common life would usually be
regarded as falling within this definition of relevancy, are excluded
from it by the Law of Evidence except in certain cases :

" I . Facts similar to, but not specifically connected with each
other. (jR.es inter alias actae.^

" 2. The fact that any person not called as a witness has asserted
the existence of any fact. (Hearsay.)

"3. The fact that any person is of opinion that a fact exists.
(Opinion.)

"4. The fact that a person's character is such as to render
conduct imputed to him probable or improbable. (Character.)

" To each of these four exclusive rules there are, however, im-
portant exceptions, which are defined by the Law of Evidence." ^

1 Stephen's Digest, p. 247.

2 /^/^.j p. xiii.

Inductive Arguments. 145

It is plain that the reason that " hearsay is not
evidence " is that to accept hearsay is to violate the
fundamental rule of inductive logic, which is, Make
sure of your observations. All the other rules of exclu-
sion are, in like manner, based upon scientific grounds.
The whole progress of judicial science, in the trying of
cases, is but an increase of precision in applying the
principles of inductive logic.

CHAPTER XV.

FALLACIES.

We cannot open the subject of Fallacies in a more
interesting way than by introducing Bacon's classic
discussion of the "Idols" in his Novum Orgamim: —

XXXIX.

"There are four classes of Idols which beset men's minds.
To these for distinction's sake I have assigned names, — calling
the first class Idols of the Tribe; the second, Idols of the Cave j
the third, Idols of the Market-place ; the fourth, Idols of the
Theatre.

XL.

" The formation of ideas and axioms by true induction is no
doubt the proper remedy to be applied for the keeping off and
clearing away of idols. To point them out, however, is of great
use ; for the doctrine of Idols is to the Interpretation of Nature
what the doctrine of the refutation of Sophisms is to common
Logic.

XLI.

" The Idols of the Tribe have their foundation in human nature
itself, and in the tribe or race of men. For it is a false assertion
that the sense of man is the measure of things. On the contrary,
all perceptions as well of the sense as of the mind are according
to the measure of the individual and not according to the measure
of the universe. And the human understanding is like a false
mirror, which, receiving rays irregularly, distorts and discolours
the nature of things by mingling its own nature with it.

Fallacies. 1 47

XLII.

" The Idols of the Cave are the idols of the individual man.
For every one (besides the errors common to human nature in
general) has a cave or den of his own, which refracts and dis-
colours the light of nature ; owing either to his own proper and
peculiar nature ; or to his education and conversation with others ;
or to the reading of books, and the authority of those whom he
esteems and admires ; or to the differences of impressions, accord-
ingly as they take place in a mind preoccupied and predisposed
or in a mind indifferent and settled ; or the like. So that the
spirit of man (according as it is meted out to different individuals)
is in fact a thing variable and full of perturbation, and governed
as it were by chance. Whence it was well observed by Heraclitus
that men look for sciences in their own lesser worlds, and not in
the greater or common world.

XLIII.

"There are also Idols formed by the intercourse and associa-
tion of men with each other, which I call Idols of the Market-
place, on account of the commerce and consort of men there.
For it is by discourse that men associate ; and words are imposed
according to the apprehension of the vulgar. And therefore the
ill and unfit choice of words wonderfully obstructs the understand-
ing. Nor do the definitions or explanations wherewith in some
things learned men are wont to guard and defend themselves, by
any means set the matter right. But words plainly force and
overrule the understanding, and throw all into confusion, and lead
men away into numberless empty controversies and idle fancies.

XLIV.

" Lastly, there are Idols which have immigrated into men's
minds from the various dogmas of philosophies, and also from
wrong laws of demonstration. These I call Idols of the Theatre ;
because in my judgment all the received systems are but so many
stage-plays, representing worlds of their own creation after an

I4S Inductive Logic.

unreal and scenic fashion. Nor is it only of the systems now in
vogue, or only of the ancient sects and philosophies, that I speak ;
for many more plays of the same kind may yet be composed and
in like artificial manner set forth ; seeing that errors the most
widely different have nevertheless causes for the most part alike.
Neither again do I mean this only of entire systems, but also of
many principles and axioms in science, which by tradition,
credulity, and negligence have come to be received.

"But of these several kinds of Idols I must speak more largely
and exactly, that the understanding may be duly cautioned.

XLV.

" The human understanding is of its own nature prone to sup-
pose the existence of more order and regularity in the world than
it finds. And though there be many things in nature which are
singular and unmatched, yet it devises for them parallels and con-
jugates and relatives which do not exist. Hence the fiction that
all celestial bodies move in perfect circles ; spirals and dragons
being (except in name) utterly rejected. Hence, too, the element
of Fire with its orb is brought in, to make up the square with the
other three which the sense perceives. Hence, also, the ratio of
density of the so-called elements is arbitrarily fixed at ten to one.
And so on of other dreams. And these fancies affect not dogmas
only, but simple notions also.

XLVI.

"The human understanding when it has once adopted an
opinion (either as being the received opinion or as being agreeable
to itself) draws all things else to support and agree with it. And
though there be a greater number and weight of instances to be
found on the other side, yet these it either neglects and despises,
or else by some distinction sets aside and rejects ; in order that by
this great and pernicious predetermination the authority of its
former conclusions may remain inviolate. And, therefore, it was
a good answer that was made by one who, when they showed him
hanging in a temple a picture of those who had paid their vows as

Fallacies. 149

having escaped shipwreck, and would have him say whether he did
not now acknowledge the power of the gods, — 'Aye,' asked he
again, ' but where are they painted that were drowned after their
vows ? ' And such is the way of all superstition, whether in
astrology, dreams, omens, divine judgments, or the like ; wherein
men, having a delight in such vanities, mark the events where they
are fulfilled, but where they fail, though this happen much of tener,
neglect and pass them by. But with far more subtlety does this
mischief insinuate itself into philosophy and the sciences ; in
which the first conclusion colors and brings into conformity with
itself all that come after, though far sounder and better. Besides,
independently of that delight and vanity which I have described,
it is the pecuHar and perpetual error of the human intellect to be
more moved and excited by affirmatives than by negatives ; whereas
it ought properly to hold itself indifferently disposed towards both
alike. Indeed, in the establishment of any true axiom, the nega-
tive instance is the more forcible of the two.

XLVII.

"The human understanding is moved by those things most
which strike and enter the mind simultaneously and suddenly, and
so fill the imagination ; and then it feigns and supposes all other
things to be somehow, though it cannot see how, similar to those
few things by which it is surrounded. But for that going to and
fro to remote and heterogeneous instances, by which axioms are
tried as in the fire, the intellect is altogether slow and unfit, unless
it be forced thereto by severe laws and overruling authority.

XLIX.

"The human understanding is no dry light, but receives an
infusion from the will and affections ; whence proceed sciences
which may be called ' sciences as one would.' For what a man
had rather were true he more readily believes. Therefore he
rejects difficult things from impatience of research ; sober things,
because they narrow hope ; the deeper things of nature, from
superstition ; the light of experience, from arrogance and pride,
lest his mind should seem to be occupied with things mean and

150 Inductive Logic.

transitory ; things not commonly believed, out of deference to the
opinion of the vulgar. Numberless, in short, are the ways, and
sometimes imperceptible, in which the affections color and infect
the understanding.

" But by far the greatest hindrance and aberration of the human
understanding proceeds from the dulness, incompetency, and
deceptions of the senses ; in that things which strike the sense
outweigh things which do not immediately strike it, though they
be more important. Hence it is that speculation commonly ceases
where sight ceases ; insomuch that of things invisible there is little
or no observation. Hence all the working of the spirits inclosed
in tangible bodies lies hid and unobserved of men. So, also,
all the more subtle changes of form in the parts of coarser
substances (which they commonly call alteration, though it is in
truth local motion through exceedingly small spaces) is in hke
manner unobserved. And yet unless these two things just men-
tioned be searched out and brought to light, nothing great can be
achieved in nature, as far as the production of works is concerned.
So, again, the essential nature of our common air, and of all bodies
less dense than air (which are very many), is almost unknown.
For the sense by itself is a thing infirm and erring ; neither can
instruments for enlarging or sharpening the senses do much ; but
all the truer kind of interpretation of nature is effected by instances
and experiments fit and apposite; wherein the sense decides
touching the experiment only, and the experiment touching the
point in nature and the thing itself." ^

Since Inductive Logic includes all the deductive
processes, it is liable to all of the fallacies treated of in
works upon that branch. The fallacies peculiar to
inductive logic are those which concern Observation
and the making of primary inductions.

I. Non-observation, or Prejudice. — All induction
being based upon observation, any opinion about facts

1 Bacon's Works, vol. viii, p. ']() sq.

Fallacies. 151

which does not begin in that way must be groundless.
The student of nature must not enter the field of inves-
tigation provided with broad generalizations ; as, that
the effect must resemble the cause ; that whatever is
inconceivable is false ; that the distinctions in nature
correspond to the received distinctions in language, etc.
A student of the Holy Scriptures, for instance, is not
at liberty (although assured of the divine origin of
Christianity by personal experience of its power) to lay
down the dictum that a revelation from the God of
truth can be mixed with none of the scientific errors
of the times in which it was given. Nor can a student
of anthropology, impressed with the dignity of man,
assert, without examination, that we are not descended
from ape-like ancestors, with pointed ears and long
tails.

But, since observation is laborious, and the mind is
impatient for conclusions, all men are tempted to excuse
themselves from the fatigue of examination and to taste
at once the pleasure of feeling that they know.

The most eminent leaders of inductive science have
not escaped this fallacy.

" Aristotle held some peculiar notions with respect to the skull.
He says, 'that part of the head which is covered with hair is
called the cranium ; the fore part of this is called the sinciput ;
this is the last formed, being the last part in the body which
becomes hard.' He correctly alludes here to the opening in the
frontal bone of a young infant, which gradually becomes hardened
by ossification ; 'the hinder part is the occiput, and between the
occiput and sinciput is the crown of the head ; the brain is placed
beneath the sinciput, and the occiput is empty (!). The skull has
sutures; in women there is but one, placed in a circle (!) ; men have
generally three joined in one, and a man's skull has been seen

152 Inductive Logic.

without any sutures at all' The often-repeated question as to how
far Aristotle's observations are the result of his own investigation,
naturally suggests itself again here ; had Aristotle ever dissected
a human body, he never would have asserted a proposition so
manifestly false as that the back of the head is empty, or that
women have only one suture placed in a circle." ^

Another example can be taken from the Novum
Organum itself: —

"Again, it has been observed that small wooden arrows without
an iron point, discharged from large engines, pierce deeper into
wooden material (say the sides of ships, or the like) than the
same arrows tipped with iron, on account of the similarity of sub-
stance between the two pieces of wood ; although this property
had previously been latent in the wood." ^

One variety of prejudice is the unquestioning accept-
ance of an opinion as to facts upon the Authority of
some great man. In early life, all must receive many
things upon the authority of parents and teachers.
But the purpose of education is wholly to remove this
dependence, so that the adult man shall know the
grounds of his own beliefs. The Protestant Reforma-
tion was much more than merely a theological or
religious movement ; it was an intellectual revolt against
authority. Advancing thought cannot leave any part of
the field of facts outside the scrutiny of inductive
science, not even the facts of religion ; for in the
domain of science there is no pope. But many Protes-
tants still bow to authority, and those most independent
of the authority of tradition often accept without ques-

1 Quoted by Fowler from the Quarterly Review for January, 1865.
Inductive Logic, p. 262.

2 Page 226.

Fallacies.

153

tion the dicta of the supposed prophets of advanced
thought.

In the best schools of the present day, the teacher
imposes no dogmas by virtue of his own authority; he
claims no exhaustive and finished knowledge of his
subject. Simply as an older investigator, he invites the
pupil to inspect the results already reached, and to take
a place beside his teacher at the boundary of knowl-
edge, and push it further outwards. That teacher fails
in his most important duty, who does not impress his
students with the present incompleteness of his science,
and the inadequacy of all the text-books in use. It
was Agassiz's custom to give to the beginner a fish and
require him to look at it for himself ; so great a teacher
never made the mistake of substituting his own books
for the book of nature.

" But an undiscriminating submission to the authority of con-
temporaries, of which I have hitherto exclusively spoken, has
been but a slight source of error when compared with undis-
criminating submission to the authority of past generations. The
latter involves a kind of compound fallacy. The authority of an
Aristotle or a Galen has come, by the process already described,
to be received without question and without limit by his own or by
the succeeding generation ; and then, by the constant repetition
of a similar process, it is received from that generation by the
leading minds of the next, from them by their contemporaries, and
so on, respect for tradition being blended with respect for a great
name, and both these resting for their support on the deference
paid to established authority. Many of the propositions accepted
without the slightest hesitation by previous generations on this
kind of authority now appear to us patently absurd, nor is it with-
out effort that we can realize the universahty of their former
reception." ^

1 Fowler's Inductive Logic, p. 292.

154 hidiLctive Logic.

" Of this tendency we have many ^ glaring instances,' as Bacon
would call them. The error has been, so to say, canonized in the
proverb ^ Malle/n cum Platone errare.'^ There is a characteristic
anecdote of Scheiner, who contests with Galileo the honor of hav-
ing been the first to observe the spots on the sun. Scheiner was
a monk ; and, on communicating to the superior of his order the
account of the spots, he received in reply from that learned father
a solemn admonition against such heretical notions : ' I have
searched through Aristotle,' he said, ^ and can find nothing of the
kind mentioned ; be assured, therefore, it is a deception of your
senses, or of your glasses.' " ^

II. Partial Observation, or the Neglect of Negative
Instances. — This is the most subtle and dangerous of
all the fallacies, and the hardest to correct. Practi-
cally, the section which treats of this fallacy is the
most important one in any text-book of inductive
logic. As soon as a few similar phenomena are
perceived, the mind moves naturally toward a primary
induction. Having observed that this A and that A
and the other A are X, the generalization is suggested
that all ^'s are X ; sometimes, indeed, a single case is
enough to beget an opinion. When this opinion has
been a little while entertained, the minds of most per-
sons seem almost wholly to lose the power to notice the
cases in which an A is not X ; every positive instance
is observed, and confirms the conviction, but the nega-
tive instances are either entirely overlooked, or else
lightly explained away.

The following case is taken from Brachet's Historical
Grammar of the French Tongite : —

1 Baden Powell's History of N'atiiral Philosophy, p. 171. Quoted in

Fowler's Inductive Logic, p. 292.

Fallacies. 155

" The tendency to simplify and reduce the number of cases was
early felt in the popular Latin ; the cases expressed shades of
thought too delicate and subtle for the coarse mind of the Bar-
barian. And so, being unable to handle the learned and compli-
cated machinery of the Latin declensions, he constructed a system
of his own, simplifying its springs, and reducing the number of the
effects at the price of frequently reproducing the same form.
Thus the Roman distinguished by means of case-terminations the
place where one is, from the place to which one is going : ^ veniunt
ad domum,' 'sunt in domo.' But the Barbarian, unable to grasp
these finer shades, saw no use in this distinction, and said, in
either case alike, 'sum in domum,' 'venio ad domum.'

" Thus, from the fifth century downwards, long before the first
written records of the French language, popular Latin reduced the
number of cases to two : (i) The nominative to mark the subject;
and (2) that case which occurred most frequently in conversation,
the accusative, to mark the object or relation. From that time
onwards the Latin declension was reduced to this : — subject,
murus ; object, muru7n.

" The French language is the product of the slow development
of popular Latin ; and French grammar, which was originally
nothing but a continuation of the Latin grammar, inherited, and in
fact possessed from its infancy, a completely regular declension;
subject, murs^ uturiLS j object, inur, muritin j and people said,
' ce imtrs est haut '; ' j'ai construit un inur.''

" This declension in two cases forms the exact difference between
ancient and modern French. It disappeared in the fourteenth
century, not without leaving many traces in the language, which
look like so many insoluble exceptions, but find their explanation
and historic justification in our knowledge of the Old French
declension." 1

Here it will be observed that the single instance of
change from the full declension of nouns in Latin to

1 Dr. Kitchin's Trans., p. 88. Seventh Edition, pp. 98-100, mistakenly
quoted by Dr. Fowler {^Inductive Logic, p. 201) as an illustration of con-
comitant variations.

156 Inductive Logic.

the non-inflection of nouns in French has suggested to
M. Brachet the generalization that barbarians cannot
readily understand and handle declensions. This is, of
course, in the face of the negative facts that these same
barbarians spoke the inflected Teutonic languages, that
fully inflected languages are found among barbarians in
Africa, in Arabia, and in all parts of the earth ; indeed,
that the history of the most cultivated languages has
been to pass from full inflection in barbarous times to
less inflection in days of civilization. He who would
hear the most delicate inflections of the Arabic, used
with precision, must go among the illiterate sons of the
desert, not into the cities. Yet very few of the readers
of M. Brachet' s most interesting work ever think of
these negative instances. There is, to most persons,
something distasteful in assuming a critical attitude
toward an author; ingenious and pleasing generaliza-
tions find with ordinary readers unchallenged accept-
ance.

This fallacy is peculiarly safe from detection when, in
a generalization, we have mistakenly put species for
genus. For example, it was believed by many gram-
marians of the last generation that the Greek Aorist
tense, which almost exactly corresponds in meaning to
the English preterite, "denotes a single or momentary
action." Instances in which single or momentary
actions were expressed in the aorist were common
enough. The fallacy was exactly like that of assuming
that all Americans are Virginians, or more precisely,
that the name Americans belongs most naturally and
properly to Virginians, because Virginians are Ameri-
cans. Such cases as "These all died," where the verb

Fallacies, 157

is aorist, were explained as viewing a single instance
as representative ; cases like " He abode two whole
years in his own hired dwelling " were overlooked.
Eminent theologians went so far as to base the proof
of the doctrine that "we all sinned in Adam" on the
fact that St. Paul uses the aorist in saying " all sinned " ;
and since that must " denote a single and momentary
action " of the whole race, it could, of course, be
nothing else than eating the forbidden fruit in the
garden of Eden.

A very common definition of a verb in the grammars
of our public schools is, "A verb is a word which
expresses action, being, or state." Hundreds of teach-
ers have taught this definition to their pupils without
noticing that the three words "action," "being," and
"state" in the definition are all negative instances;
they express action, being, and state, and yet are not
verbs. Such nouns as love, hate, murder, theft, peace,
existence, etc., appear on every page, and yet it never
occurs to these teachers that, according to their defini-
tion, these words should be verbs. The fallacy is in
taking that for a mark of a species which is the mark
of the genus in which the species is included, and which
the species in question shares with others.

" We would strongly recommend to any of our readers whose
occupations lead them to attend to the ' signs of the weather,' and
who, from hearing a particular adage often repeated, and from
noticing themselves a few remarkable instances of its verification,
have ' begun to put faith in it,' to commence keeping a note-book,
and to set down without bias all the instances which occur to them
of the recognized antecedent, and the occurrence or non-occurrence
of the expected consequent, not omitting, also, to set down the
cases in which it is left undecided; and, after so collecting a

158 Inductive Logic.

number of instances (not less than a hundred), to proceed to form
his judgment on a fair comparison of tlie favorable, the unfavor-
able, and the undecided cases ; remembering always that the
absence of a majority one way would be in itself an improbability^
and that, therefore, to have any weight, the majority should be a
very decided one, and that not only in itself, but in reference to
the neutral instances. We are all involuntarily much more strongly
impressed by the fulfilment than by the failure of a prediction, and
it is only, when thus placing ourselves face to face with fact and
experience, that we can fully divest ourselves of this bias." ^

III. Malobservation. — It is possible to make care-
ful observations, but to misunderstand what we observe.
The simple sensations which the brain receives are
interpreted in accordance with primary inductions more
or less inexact. The far greater part of all our so-called
observations are necessarily inferences, and we are
often most in error when acting upon what seems the
direct evidence of our own senses. Here is an example
from the Novum Organum : —

" On this subject, therefore, we may take the following as an
Instance of the Fingerpost. We see in large fires how high the
flames ascend ; for the broader the base of the flame, the higher
is its vertex. Thus extinction appears to commence at the sides,
where the flame is compressed and troubled by the air. But the
heart of the flame, which is not touched by the air but surrounded
by other flame on all sides, remains numerically identical ; nor is
it extinguished until gradually compressed by the surrounding air.
Thus all flame is in the form of a pyramid, being broader at the
base where the fuel is, but sharp at the vertex, where the air is
antagonistic and fuel is wanting. But smoke is narrow at the
base, and grows broader as it ascends, like an inverted pyramid ;
the reason being that the air admits smoke and compresses flame.

1 Sir John Herschel's Familiar Lectiires on Scientific Subjects, Lecture
IV, quoted by Fowler, Inductive Logic, p. 257.

Fallacies, 159

For let no one dream that lighted flame is air, when in fact they
are substances quite heterogeneous." ^

Bacon in this instance did not really see what he
thought he saw. Other illustrations have been already
given in the chapter on Observation (page 9).

IV. Mistake in Ai'ea. — A primary induction may be
correct, but we may mistake its area. It is important
to know whether the instances examined have come at
random from all parts of the field regarding which we
generalize. Before deciding that all lobsters are red,
the inquirer must be sure that all his observations have
not been confined to boiled specimens. Often it is
possible to be sure of an induction over a certain area,
while it is held as only provisionally true over a broader
field. Here comes in the principle which justifies the
applying of inductions to what are called ^^ adjacent
cases!' Since at any moment it is unlikely that we
have reached the boundary of our territory, there are
probably at least a few more cases of the same sort
between us and that boundary. If we find ourselves
upon a line of uniformity, it is improbable that we have
struck it just at the end. A traveler from Liverpool
to London, having for fifty miles observed red poppies
growing in the grain fields, will expect to see some
more red poppies ; but he will not have so positive an
expectation of seeing them all the way to the capital.

Hume says : —

" The Indian prince, who refused to believe the first relations
concerning the effects of frost, reasoned justly ; and it naturally
required a very strong testimony to engage his assent to facts that

1 Page 267.

i6o Inductive Log-ic

arose from a state of nature with which he was unacquainted, and
which bore so little analogy to those events of which he had
constant and uniform experience. Though they were not con-
trary to his experience, they were not conformable to it."

The Indian prince simply made a mistake as to the
area regarding which his observations qualified him to
affirm ; and that is precisely the mistake of Hume
himself, in his famous argument against miracles.

The ancients made this error in studying the laws of
motion. Mr. Mill says : —

" This assertion [that all bodies in motion continue to move in
a straight line with uniform velocity until acted upon by some new
force] is in open opposition to first appearances ; all terrestrial
objects, when in motion, gradually abate their velocity, and at
last stop ; which, accordingly, the ancients, with their inductio
per enumerationem siinplicejn^ imagined to be the law." ^

The induction which the ancients made was correct,
and was made in the only possible way ; they only
mistook its area. What they established was the
universal truth under ordinary conditions ; their error
was in supposing that the truth held under all condi-
tions.

V, Mistake in Isolation. — The rules for isolating
facts of causation seem so simple, their applica-
tion seems so easy, and their results seem so sure,
that we are likely to forget how much their value is
diminished by the difficulty of ascertaining whether we
have taken account of all relevant circumstances. Dr.
Fowler says: —

"A bullet is fired from a gun, or a dose of prussic acid is
administered, and an animal instantly falls down dead. There is

1 Logic, p. 290.

Fallacies. i6i

no hesitation in ascribing the death to the gun-shot wound or the
dose of poison. Nor is this confidence the effect of any wide
experience, for if it were the first time that we had seen a gun
fired, or a dose of poison administered, we should liave no hesita-
tion in ascribing the altered condition of the animal to this novel
cause ; we should know that there was only one new circumstance
operating upon it, and consequently, that any change in its condi-
tion must be due to that one circumstance." ^

This analysis is wholly incorrect. When a man falls
dead on the street we are at a loss for a cause. Many
events, observable and unobservable, are occurring at
the same time ; the man may have had heart disease.
We proceed to make an hypothesis according to the
established rules. The first inquiry of the mind is for
some already accepted primary induction under which
to class the event. If a small boy should shoot off a
Chinese fire-cracker, and at that moment some one
should fall, we should not connect the two events,
because we already have the induction that fire-crackers
do not kill.

This impossibility of knowing always whether isola-
tion is perfect, leads to the rule that in studying any
phenomenon, we should vary the circumstances as much
as possible, and use each of the applicable methods of
proof independently. Yet even then we are liable to
err, as the following example shows : —

" Thales of Miletus, who lived in the sixth century B.C., and
who was called Hhe first of natural philosophers ' by TertuUian,
and ^ the first who inquired after natural causes ' by Lactantius,
affirmed that water was the first principle of things, perhaps,
according to some writers, because Homer had made Okeanos the
source of the gods. At least we are reminded of the boundless

1 hiductive Logic, p. 151.

1 62 Inductive Logic.

watery chaos of older cosmogonies. This doctrine of Thales was
not without its supporters during the Middle Ages, and, indeed, the
convertibility of water into earth and air was not absolutely dis-
proved until about a century ago. One of the ablest supporters
of the dogma was Van Helmont (b. 1577, d. 1644), who affirmed
that all metals, and even rocks, may be resolved into water ; animal
substances are produced from it, because fish live upon it ; and
vegetable substances may also be produced from it. This asser-
tion he endeavored to prove by what would appear to be a very
conclusive experiment in those days, when neither the composition
of the air nor of water was known. . He took a willow which
weighed five pounds, and planted it in two hundred pounds of
earth, which he had previously carefully dried in an oven. The
willow was frequently watered, and at the end of five years he
pulled it up and found that its weight amounted to one hundred
and sixty-nine pounds and three ounces. The earth was again
dried and was found to have lost only two ounces. Thus it
appeared that 164 pounds of wood, bark, roots, leaves, etc., had
been produced from water alone. Hence he inferred that all
vegetables are produced from water alone ; not knowing, as was
afterwards proved by Priestley, that a constituent of the atmosphere,
called carbonic acid, had furnished the soKd part of the tree,
although, indeed, there was much water with it." ^

This experiment of Van Helmont was, so far as he
could know, a rigorous application of the famous test
of difference ; yet it wholly failed to teach the truth,
because the supposed isolation was unreal.

Under this head belongs the well-known fallacy Post
hoc, ergo propter hoc. No one would have the hardi-
hood to argue that since the group of antecedents
ABCDEFGHIJK have been followed by the conse-
quents Imnopqrstuv, therefore C must be the cause of
q ; but it is often convenient for a crank or a dema-
gogue to fasten attention upon the fact that after C

1 Rodwell's Birth of Chemistry, p. 14.

Fallacies. 163

followed q, the unspoken assumption being that isolation
is conceded, that C was the only new antecedent, and q
the only new consequent. Thus, it is a familiar fact in
politics that hard times, whatever may have been their
causes, discredit the party in power, the outs arguing
that since the present administration came into office
money has been scarce, and wholly omitting to refer to
speculation, drought, or any other cause of financial
depression.

It is a mistake in isolation to overlook the MttUiality
of Cause and Effect. This is illustrated in the following
remarks of Sir G. C. Lewis: —

" An additional source of error in determining political causa-
tion is likewise to be found in the mutuality of cause and effect.
It happens sometimes that when a relation of causation is estab-
lished between two facts it is hard to decide which, in the given
case, is the cause and which the effect, because they act and react
upon each other, each phenomenon being in turn cause and effect.
Thus, habits of industry may produce wealth ; while the acquisi-
tion of wealth may promote industry ; again, habits of study may
sharpen the understanding, and the increased acuteness of the
understanding may afterward increase the appetite for study. So
the excess of population may, by impoverishing the laboring classes,
be the cause of their living in bad dwellings ; and, again, bad
dwellings, by deteriorating the moral habits of the poor, may
stimulate population. The general intelligence and good sense of
the people may promote its good government, and the goodness of
the government may in its turn increase the intelligence of the
people, and contribute to the formation of sound opinions among
them. Drunkenness is in general the consequence of a low degree
of intelligence, as may be observed both among savages and in
civilized countries. But, in return, a habit of drunkenness pre-
vents the cultivation of the intellect, and strengthens the cause out
of which it grows. As Plato remarks, education improves nature,
and nature facilitates education. National character, again, is

164 Inductive Logic.

both effect and cause ; it reacts on the circumstances from which
it arises. The national pecuharities of a people, its race, physical
structures, climate, territories, etc., form originally a certain char-
acter, which tends to create certain institutions, political and
domestic, in harmony with that character. These institutions
strengthen, perpetuate, and reproduce the character out of which
they grew, and so on in succession, each new effect becoming, in
its turn, a new cause. Thus a brave, energetic, restless nation,
exposed to attack from neighbors, organizes military institutions :
these institutions promote and maintain a warlike spirit ; this
warlike spirit, again, assists the development of the military
organization, and it is further promoted by territorial conquests
and success in war, which may be its result — each successive
effect thus adding to the cause out of which it sprung." ^

1 On Methods of Observation a7id Reasoning in Politics, vol. i, p. 375,
quoted by Fowler, Inductive Logic, p. 322.

CHAPTER XVI.
THE WORK OF BACON.

Two great names stand out conspicuous beyond all
others in the development of Inductive Logic : they are
those of Bacon and of Mill. Of the latter enough has
already been said to give the reader a knowledge of the
main points of his doctrine. The last chapter contains
a long quotation which well represents the style of the
Novum Organum. But it seems undesirable to close
this book without devoting a brief chapter to an esti-
mate of the debt which we owe to that " Prince of
Philosophers," who, with the " Prince of Poets," accord-
ing to Lord Macaulay, "made the Elizabethan age a
more glorious and important era in the history of the
human mind than the age of Pericles, of Augustus, or
of Leo."

Francis Bacon, Baron Verulam (i 561-1626), is com-
monly regarded as the founder of modern inductive
science. Reid expresses this opinion as follows : —

" After man had labored in the search of truth near two thou-
sand years by the help of Syllogisms, Lord Bacon proposed the
method of Induction a^ a more effectual engine for that purpose.
His Novinn Orgamcin gave a new turn to the thoughts and labors
of the inquisitive, more remarkable and more useful thsn that
which the Organon of Aristotle had given before, and may be
considered a second grand era in the progress of humau nature." ^

1 Hamilton's Reid, p. 712 ; quoted by Minto, Logic, p. 244.

1 66 Inductive Logic.

This is Bacon's own claim ; he says : —

"All those who before me have applied themselves to the
invention of arts have but cast a glance or two upon facts and
examples and experience, and straightway proceeded, as if inven-
tion were nothing more than an exercise of thought, to invoke
their own spirits to give them oracles. I, on the contrary, dwell-
ing purely and constantly among the facts of nature, withdraw my
intellect from them no further than may suffice to let the images
and rays of natural objects meet in a point, as they do in the sense
of vision ; whence it follows that the strength and excellency of
the wit has but little to do in the matter. And the same humihty
which I use in inventing I employ likewise in teaching. For I do
not endeavor either by triumphs of confutation, or pleadings of
antiquity, or assumption of authority, or even by the veil of
obscurity, to invest these inventions of mine with any majesty ;
which might easily be done by one who sought to give lustre to
his own name rather than light to other men's minds. I have not
sought (I say), nor do I seek either to force or ensnare men's
judgments, but I lead them to things themselves and the concord-
ances of things, that they may see for themselves what they have,
what they can dispute, what they can add and contribute to the
common stock. And for myself, if in anything I have been either
too credulous, or too httle awake and attentive, or if I have fallen
off by the way and left the inquiry incomplete, nevertheless I so
present these things naked and open, that my errors can be
marked and set aside before the mass of knowledge be further
infected by them ; and it will be easy, also, for others to continue
and carry on my labors. And by these means I suppose that I
have established forever a true and lawful marriage between
the empirical and rational faculty, the unkind and ill-starred
divorce and separation of which has thrown into confusion all the
affairs of the common family." ^

The claim of Bacon to be the very first cannot be
allowedj but he remains the great prophet and leader of
inductive investigation.

1 Preface to the Nozuon Organum.

The Work of Bacon. 167

The truth is thus stated by Minto : —

" Undoubtedly Bacon's powerful eloquence and high pohtical
position contributed much to make the study of Nature fashionable.
He was high in place and great in intellect, one of the command-
ing personalities of his time. Taking ' all knowledge for his
province,' though study was really but his recreation, he sketched
out a plan of universal conquest with a clearness and confidence
that made the mob eager to range themselves under his leadership.
He was the magnificent demagogue of science. There had been
champions of ' Induction' before him, but they had been compara-
tively obscure and tongue-tied.

"While, however, we admit to the full the great services of this
mighty advocate in making an ^ Inductive ' method popular, we
should not forget that he had pioneers even in hortatory leader-
ship. His happiest watchword, the Interpretation of Nature, as
distinguished from the Interpretation of Authoritative Books, was
not his invention. If we read Whewell's History of the Iiidiictive
Sciences^ we shall find that many before him had aspired to 'give
a new turn to the labors of the inquisitive,' and in particular to
substitute inquisition for disquisition.

" One might compile from Whewell a long catalogue of eminent
men before Bacon who held that the study of Nature was the
proper work of the inquisitive : Leonardo da Vinci (1452-15 19),
one of the wonders of mankind for versatility, a miracle of excel-
lence in many things, painter, sculptor, engineer, architect, astrono-
mer, and physicist; Copernicus (1473-1543), the author of the
Heliocentric theory ; Telesius (i 508-1 588), a theoretical reformer,
whose De Remtin Natiira (1565) anticipated not a little of the
N'ovum Orgaiiitm J Cesalpinus (i 520-1 603), the Botanist ; Gilbert
(i 540-1 603), the investigator of Magnetism. By all these men
experiment and observation were advocated as the only way of
really increasing knowledge. They all derided mere book-learning.
The conception of the world of sense as the original MS. of which
systems of philosophy are but copies, was a familiar image with
them-" 1

1 Minto's Logic, Inductive and Dedicctive, pp. 245, 246.

1 68 Inductive Logic.

Mr. Mill has made the following judicious criticism
upon the work of Bacon:-—

" It has excited the surprise of philosophers that the detailed
system of inductive logic, which this extraordinary man labored
to construct, has been turned to so little direct use by subsequent
inquirers, having neither continued, except in a few of its gener-
alities, to be recognized as a theory, nor having conducted in
practice to any great scientific results. But this, though not
unfrequently remarked, has scarcely received any plausible explana-
tion ; and some, indeed, have preferred to assert that all rules of
induction are useless, rather than suppose that Bacon's rules are
grounded upon an insufficient analysis of the inductive process.
Such, however, will be seen to be the fact, as soon as it is con-
sidered, that Bacon entirely overlooked Plurahty of Causes. All
his rules imply the assumption, so contrary to all we now know
of nature, that a phenomenon cannot have more than one cause.

" When Bacon is inquiring into what he terms i\\Q forma calidi
aut frigidi^ gravis aut levis^ sicci aut humidi^ and the like, he
never for an instant doubts that there is some one thing, some
invariable condition, or set of conditions, which is present in all
cases of heat, or of cold, or of whatever other phenomenon he is
considering ; the only difficulty being to find what it is ; which,
accordingly, he tries to do by a process of elimination, rejecting
or excluding, by negative instances, whatever is not the fo7'7na or
cause, in order to arrive at what is. Butj^ that tliis forma or
cause is one thing, and that it is the same in all hot objects, he
has no more doubt of than another person has that there is always
some cause or other. In the present state of knowledge it could
not be necessary, even if we had not already treated so fully of the
question, to point out how widely this supposition is at variance
with the truth. It is particularly unfortunate for Bacon that,
falling into this error, he should have fixed almost exclusively
upon a class of inquiries in which it was especially fatal, namely,
inquiries into the causes of the sensible qualities of objects. For
his assumption, groundless in every case, is false in a peculiar
degree with respect to those sensible qualities. In regard to
scarcely any of them has it been found possible to trace any unity

The Work of Bacon. 169

of cause, any set of conditions invariably accompanying the
quality. The conjunctions of such quaUties with one another
constitute the variety of Kinds, in which, as already remarked,
it has not been found possible to trace any law. Bacon was
seeking for what did not exist. The phenomenon of which he
sought for the one cause has oftenest no cause at all, and when it
has, depends (as far as hitherto ascertained) upon an unassignable
variety of distinct causes." 1

1 Logic, p. 532.

INDEX.

Adjacent cases, 159.

Agassiz, 50, 153.

Agreement, canon for test of, 99.

method of, 104.

Agreement and difference, method
of, 104.

Ancient and modern thinking, 113.

Anima and dme, 43.

Aorist tense, 156.

Applied sciences, 2.

Area, mistake in, 159.

Argument from facts of resem-
blance, 42.

Arguments, inductive, 129.

Aristotle on the skull, 15.

Athletic training, 96.

Authority, 152.

Bacon, work of, 165.

claim of, 166.

on " Idols," 146.

on observation, 9.

Bain quoted, 21.

views discussed, 23, 31.

Barbarians and inflections, 156.
Blucher at Waterloo, 109.
Botanical names, 53.
Botany, 48.
Brachet quoted, 154.
Butler quoted, 129.

Canons for isolating, 91.
Canon for test of difference, 93.
for test of agreement, 99.

Cases under Canon First, 94.

under Canon Second, loi.

Cato, 141.
Causation, 55, 71.

Mill's doctrine of, 75.

Cause simultaneous with effect, 84.

the sum of conditions, 85.

Chemical nomenclature, 53.

Chinamen, 40.

Classes of inductions, 31.

Classification, 52.

Cliffs of England, 17.

Coexistence, facts of, 7, 47.

Color in animals, 39.

Comprehensive cause, 91.

Concomitant variations, 105, iii.

Conditional cause, 61.

Copernicus, 37.

Correction of instances, 106.

Cretans, 17.

Crows, 17, 38, 115.

Crucial instances, 39.

Crusoe, Robinson, 133.

Crystallization, 108.

Dana on coral islands, 121.
Darwin quoted, 11, 69, 117.

on coral islands, 121.

on species, 51.

Davis quoted, 16, 73, 126.

on induction, 31.

Deductive logic, relation to in-
ductive, 2.
Dew, cause of, no.

172

Index.

Difference, canon for test of, 93.
Discovery, 4.
Dragon not a fact, 6.

Ebullition in hydrochloric acid,

102.
Efficient cause, 64.
Empirical cause, 93.

laws, 25, 34, 116.

Energetic cause, 60.

Eohippus, 44.

Events, the causes of events, 65.

the reactions of things, 91.

Evidence at law, 139.
Exception proves the rule, 25.
Experience tests uniformities, 19.
" Experimental " not appropriate

name for Mill's methods, 107.
Explanation, 116.

Facts, 6.

of causation, 7, 55.

of coexistence, 7, 47.

of relation, 6.

of resemblance, 7, 41.

of succession, 8, 55.

ultimate, 8.

Fallacies, 146.

Final cause, 70.

Firecracker, 161.

Forma, Bacon's inquiry for, 168.

Fowler quoted, 11, 12, 18, 43, 136,

160.
view of inductio per enume-

rationem siniplicen, 18, 30.
Formal cause, 70.
Friction, heat by, iii.

Genesis of the horse, 44.
Glacial dam at Cincinnati, 133.
Gold, 47.
Grand jury, 139.

Grant at Cold Harbor, 128.
Gratuitous hypothesis, 118.
Gray quoted, 49, 130.
Greek physical philosophy, 125.

Hazard of induction, 22.

Hearsay, 145.

Helmholtz, on hypothesis, 124.

Herschel quoted, 37, 157.

Historical cause, 66.

Horse, 44.

Hume quoted, 139, 159.

as to miracles, 160.

Huxley, 117.
Hypothesis, 37, 115.

importance of, 126.

Mill's definition, 119,

value of false, 127.

Ice and salt, 74.

" Idols," Bacon's, 146.

Inductio per emmierationem sini-
pliceni, 17, 19, 113, 160.

Induction defined, 14.

Inductions of modern science,
24.

Inductive arguments, 129.

Inductive logic defined, i.

relation to deductive, 2.

Indian prince, 1 59.

Indirect method of agreement, 104,
109.

Inference from particulars to par-
ticulars, 33.

from single instances, 38.

Iodine, 100.

Iron in oxygen, 92.

Isolating, canons for, 91.

Isolation, mistake in, 160.

Joint method of agreement and
difference, 104, 109.

Index.

173

Latin quantities, 26.
Laws of nature, 116.
Le Conte quoted, 44, 121.
Legitimate hypothesis, 118.
Lewis quoted, 163.
Linnseus, 48.
Lotze quoted, 63.

Marble in acid, 95.
Master's degree, 96.
Masts and hulls of ships, 36.
Material cause, 61.
Method of agreement, 104.

of difference, 104.

of agreement and difference,

104.

of residues, 104.

concomitant variations, 105,

III.
Mill quoted, 12, 19, 20, 31, 34, 36,

38, ^T, 78, 81, 85, 87, 103, 104,

108, no, 112, 119, 168.
Mill, cause and effect sometimes

simultaneous, 81.

definition of cause, 77.

doctrine of causation, 75.

four experimental methods,

103.

on hypothesis, 119.

on inductio per emimerationetn

simp lie em, 18.
infers from particular to par-
ticular, 2>Z-

misses sequence, 108.

on the will, 87.

on the root of the theory of

induction, 47.

vagueness of his canons, 107.

mental characteristics, 32.

Mill and river, 16.

Minto, 31, quoted, 33, 116, 167.

Mistake in area, 1 59.

Mistake in isolation, 160.
Mixed inductions, 14, 36.
Motion, laws of, 160.
Murray on coral islands, 123.
Mutuality of cause and effect, 163.

Natural kinds, 48.

Negative cause, 70.

Neglect of negative instances, 1 54.

Neptune, 120.

Newton's discoveries, 36.

Night the cause of day, 86.

Nomenclature, 53.

Non-observation, 150.

Noun or verb the cause, 109.

Observation, 9.

characteristic of induction, 9.

contrasted with experiment,

10.
Occasional cause, 68.
Opium, 43.

Partial observation, 154.

Perceptions confused with infer-
ences, 12.

Planets, 22.

Plurality of causes, 102.

Poppies, 159.

Pottery, 42.

Post hoc, ergo propter hoc, 162.

Prejudice, 150.

Present tense, 15.

Primary inductions, 14, 20, 29.

Primary rule for inductive thinking,
II.

Probable evidence, 129.

Problem of induction solved, 39.

Pure inductions, 14.

Pure sciences, 2.

Reid on Bacon, 165.
Relevancy, 142.

174

Index.

Resemblance, facts of, 7, 41.
Residue, same as difference, 106.
Residues, method of, 104.
Rodwell quoted, 162.
Rubidium, 28, 39.
Rumford quoted, 56.

his experiment discussed, 59.

Root of the theory of induction, 47.

Secondary inductions, 28.

Scheiner, 154.

Schiller quoted, 100.

Ship and iceberg, 119.

Solidification and crystallization,
109.

Socrates, 29.

Species, 49.

Agassiz on, 51.

Darwin on, 51.

De Candolle on, 51.

Gray on, 49.

States, d"].

Stephen quoted, 139, 142.

Stewart on observation, 13.

Substantive facts, 6.'

Succession confused with cau-
sation, 56, 72.

Succession, facts of, ']2,

Swans, 38.

Symbols under Canon First, 97.

under Canon Second, loi.

Siphon, 66.

Tariff, 99.

Taste and freedom, 100.
Terminology, 53.
Testimony, 139.
Theory, 115.

Things causes of events, 64.

causes of things, 64.

Touching a button, 94.
Trees, longevity of, 130.
Trials at law, 139.

Ultimate laws, 25.

properties, 55.

Unconditionalness, 85.

Uniformities, how discovered, 15.

Uniformity of nature, 19, 33, 41,
42.

Uniformity not in course of events,
20.

Unknown not discovered by rea-
soning, 3.

Vagueness of Mill's canons, 107.

Van Helmont's experiment, 161.

Varying the circumstances, 161.

Vera causa, 118.

Veracity of God, 17.

Verb defined, 157.

Verification, 136.

Vesuvius, 25.

Village matron, 33, 34.

Volitional cause, 62.

Weather on Lake Erie, 26.

signs of, 157.

Webster, 95.
Whately quoted, 4.

on induction, 30, 31.

Whewell on Greek philosophy, 125.
Will and wish, 90.
Willow, 162.
Wooden arrows, 152.
Wright quoted, 133.

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